{"id":"n-521827c5e15e2360","revision":0,"first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","name":"basis_map_A013609 of basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*3^j.","polytool_family":null,"interpretation":null,"rows_observed":15,"degree_pattern":"affine","degree_slope":1,"degree_intercept":2,"palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":true,"rows":[["484","792","324"],["10648","26136","21384","5832"],["234256","766656","940896","513216","104976"],["5153632","21083040","34499520","28226880","11547360","1889568"],["113379904","556592256","1138484160","1241982720","762125760","249422976","34012224"],["2494357888","14285867904","35065312128","47816334720","39122455680","19205569152","5237882496","612220032"],["54875873536","359187535872","1028582489088","1683134982144","1721388049920","1126726723584","460933659648","107750725632","11019960576"],["1207269217792","8889891512832","29094190405632","55543454410752","68166966776832","55772972817408","30421621536768","10667321837568","2181952194048","198359290368"],["26559922791424","217308459202560","800090236154880","1745651424337920","2499455448483840","2454010803965952","1673189184522240","782270268088320","240014741345280","43639043880960","3570467226624"],["584318301411328","5258864712701952","21513537461053440","52805955586222080","86409745504727040","98978435759960064","80982356530876416","47327351219343360","19361189135185920","5280324309596160","864053068843008","64268410079232"],["12855002631049216","126212753104846848","567957388971810816","1548974697195847680","2851521601655992320","3732901005804208128","3563223687358562304","2498884144381329408","1277838482922270720","464668539244462080","114055005087277056","16966860260917248","1156831381426176"],["282810057883082752","3008070615665516544","14766892113267081216","44300676339801243648","90615019785957089280","133451210957500440576","145583139226364116992","119113477548843368448","73092361223153885184","33223800555979038720","10873243818320412672","2426261017311166464","330853775087886336","20822964865671168"],["6221821273427820544","71268134586536853504","379016897573855084544","1240418937514434822144","2790942609407478349824","4566996997212237299712","5604950860215018504192","5240993012149108211712","3752074542788566106112","2046586114248308785152","837239774010671775744","249096131110613090304","50951481363534495744","6413473178626719744","374813367582081024"],["136880068015412051968","1679891743825511546880","9621198169182475223040","34111520781646957608960","83728278282224350494720","150710900908003830890496","205514864874550678487040","216190961751150713733120","176883514160032402145280","112562236283656983183360","55257825084704337199104","20550430816625579950080","5604662949988794531840","1058223074473408757760","123688411302086737920","6746640616477458432"],["3011361496339065143296","39421459588438670966784","241904411110873662750720","923635024241517621411840","2456029496278580947845120","4822748829056122588495872","7234123243584183882743808","8455468726267227914895360","7782874623041425694392320","5660272453121036868648960","3241792404969321115680768","1446750329490440828485632","493210339599013918801920","124164840738213294243840","21769160389167265873920","2374817497000065368064","121439531096594251776"]],"degrees":[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"row_sums":["1600","64000","2560000","102400000","4096000000","163840000000","6553600000000","262144000000000","10485760000000000","419430400000000000","16777216000000000000","671088640000000000000","26843545600000000000000","1073741824000000000000000","42949672960000000000000000"],"nonn":true,"definitions":[{"position":0,"source":"derived:basis_map_A013609","source_kind":"derived","equality_edge_id":null,"recurrence":{"first_index":0,"initial_polynomials":[["484","792","324"]],"recurrence":{"terms":[{"coeff":{"coeffs":[["22","18"]]},"deriv_order":0,"offset":1,"sign":"none"}]},"schema":"polytool.recurrence.v1"}}],"properties":[{"id":201077,"position":0,"claim":"real_rooted","from_index":0,"region_key":"(-inf, 0]","provenance":"edges","claim_data":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"label":"Real-rooted","description":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]","region_exact":null,"edges":["e-9512493cef2d9dab"]},{"id":201078,"position":1,"claim":"one_signed_coefficients","from_index":0,"region_key":null,"provenance":"derived_from_edges","claim_data":{"alternating":false,"claim":"one_signed_coefficients","from_index":0},"label":"Coefficients of one sign","description":"Every nonzero row, n >= 0: the coefficients of P_n have one sign","region_exact":null,"edges":["e-9512493cef2d9dab"]},{"id":201079,"position":2,"claim":"hadamard_kernel","from_index":0,"region_key":null,"provenance":"derived_from_edges","claim_data":{"claim":"hadamard_kernel","from_index":0},"label":"Hadamard kernel (Malo)","description":"Rows P_n, n >= 0, are Hadamard kernels (preserve real-rootedness)","region_exact":null,"edges":["e-9512493cef2d9dab"]}],"region_exact":{},"incoming_edges":[{"id":"e-9512493cef2d9dab","operation":{"map":"A013609","operation":"basis_map"},"operation_detail":"A013609","conclusion_id":"n-521827c5e15e2360","premise_count":1,"theorem":"geometric family P_k = g(t) (a + d t)^k: T(p) = g(t) p(a + d t), so the roots of T(p) are those of g and the points (r - a)/d for the roots r of p (elementary)","lean_route":null,"lean_declarations":[],"certificate_hash":"8d8e765bdddf13b2525082a228a702167fd3c8a3fd9dc506837b3b25c5d933e3","verification_polytool":"replayed","verification_lean":"not_attempted","claims":[{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}}],"premises":[{"position":0,"node_id":"n-7e380db7ce29966b","role":"sequence","name":"basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*10^(i-j)*3^j.","uses":{"claim":"real_rooted","from_index":0,"region":{"upper":{"closed":true,"value":"0"}}},"uses_text":"Every row P_n, n >= 0, is zero or real-rooted with all roots in (-inf, 0]"}]}],"used_by":[],"used_by_total":0,"links":[{"id":"l-1315624b6ff500ba","kind":"fingerprint_related","node_a_id":"n-ec8e2539152ade57","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-ec8e2539152ade57","other":{"id":"n-ec8e2539152ade57","name":"derivative of basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["198","162"],["3267","5346","2187"],["47916","117612","96228","26244"]],"card_rows":[["198","162"],["3267","5346","2187"],["47916","117612","96228","26244"],["658845","2156220","2646270","1443420","295245"]],"row_sums_preview":["360","10800","288000","7200000","172800000","4032000000","92160000000","2073600000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-cfc5b48d32898a3e","steps":["reverse","D"],"edges":["e-9b28f01504767b0f","e-bf8ca1b977f10a19"],"text":"A038301 \u2192 reverse \u2192 D"},"headline":"A038301 \u2192 reverse \u2192 D","chain":null}},{"id":"l-15c176e703140323","kind":"fingerprint_related","node_a_id":"n-b2ae2bce0e1523fc","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-b2ae2bce0e1523fc","other":{"id":"n-b2ae2bce0e1523fc","name":"basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*11^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["18","22"],["324","792","484"]],"card_rows":[["1"],["18","22"],["324","792","484"],["5832","21384","26136","10648"]],"row_sums_preview":["1","40","1600","64000","2560000","102400000","4096000000","163840000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-b7cf68162d40a956","steps":["basis A013609"],"edges":["e-59f75239fe41171d"],"text":"A038277 \u2192 basis A013609"},"headline":"A038277 \u2192 basis A013609","chain":null}},{"id":"l-6437fbc6843ee783","kind":"fingerprint_related","node_a_id":"n-3890397b83a674f9","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-3890397b83a674f9","other":{"id":"n-3890397b83a674f9","name":"derivative of Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[[],["9"],["198","162"]],"card_rows":[["9"],["198","162"],["3267","5346","2187"],["47916","117612","96228","26244"]],"row_sums_preview":["0","9","360","10800","288000","7200000","172800000","4032000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-4e096b5929fd3f2e","steps":["D"],"edges":["e-8b0042cde2dad276"],"text":"A038323 \u2192 D"},"headline":"A038323 \u2192 D","chain":null}},{"id":"l-9cc6961155e9b11a","kind":"fingerprint_related","node_a_id":"n-95452b52aae7dbf2","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-95452b52aae7dbf2","other":{"id":"n-95452b52aae7dbf2","name":"mobius_x_over_x_plus_one of basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*1^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["9","11"],["81","198","121"]],"card_rows":[["1"],["9","11"],["81","198","121"],["729","2673","3267","1331"]],"row_sums_preview":["1","20","400","8000","160000","3200000","64000000","1280000000"],"regions":["[-1, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-366b2525683554ec","steps":["basis A013609","x \u21a6 x/(x+1)"],"edges":["e-0da8e8e5bf86fd8d","e-bc0b86b7da83bbc9"],"text":"A038279 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)"},"headline":"A038279 \u2192 basis A013609 \u2192 x \u21a6 x/(x+1)","chain":null}},{"id":"l-a9bf5a245132fc7c","kind":"fingerprint_related","node_a_id":"n-6a03653d7a50bc7a","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-6a03653d7a50bc7a","other":{"id":"n-6a03653d7a50bc7a","name":"derivative of Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*11^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["198","242"],["2673","6534","3993"],["32076","117612","143748","58564"]],"card_rows":[["198","242"],["2673","6534","3993"],["32076","117612","143748","58564"],["360855","1764180","3234330","2635380","805255"]],"row_sums_preview":["440","13200","352000","8800000","211200000","4928000000","112640000000","2534400000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-cfc5b48d32898a3e","steps":["D"],"edges":["e-4169abb442691e46"],"text":"A038301 \u2192 D"},"headline":"A038301 \u2192 D","chain":null}},{"id":"l-ac83664645ae29db","kind":"fingerprint_related","node_a_id":"n-4113d906b9d95b00","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-4113d906b9d95b00","other":{"id":"n-4113d906b9d95b00","name":"basis_map_A013610 of Triangle whose (i,j)-th entry is binomial(i,j)*8^(i-j)*3^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["121","198","81"],["1331","3267","2673","729"],["14641","47916","58806","32076","6561"]],"card_rows":[["121","198","81"],["1331","3267","2673","729"],["14641","47916","58806","32076","6561"],["161051","658845","1078110","882090","360855","59049"]],"row_sums_preview":["400","8000","160000","3200000","64000000","1280000000","25600000000","512000000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-cfc5b48d32898a3e","steps":["reverse"],"edges":["e-9b28f01504767b0f"],"text":"A038301 \u2192 reverse"},"headline":"A038301 \u2192 reverse","chain":null}},{"id":"l-c2285ae1a01ad3e6","kind":"fingerprint_related","node_a_id":"n-1f17a7a2f7f54d5c","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-1f17a7a2f7f54d5c","other":{"id":"n-1f17a7a2f7f54d5c","name":"derivative of basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*11^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[[],["22"],["792","968"]],"card_rows":[["22"],["792","968"],["21384","52272","31944"],["513216","1881792","2299968","937024"]],"row_sums_preview":["0","22","1760","105600","5632000","281600000","13516800000","630784000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-b7cf68162d40a956","steps":["basis A013609","D"],"edges":["e-59f75239fe41171d","e-f8b03decdafd3042"],"text":"A038277 \u2192 basis A013609 \u2192 D"},"headline":"A038277 \u2192 basis A013609 \u2192 D","chain":null}},{"id":"l-d267f2ae6eab1e1a","kind":"fingerprint_related","node_a_id":"n-7153e756699bb014","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-7153e756699bb014","other":{"id":"n-7153e756699bb014","name":"reversal of Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["9","11"],["81","198","121"]],"card_rows":[["1"],["9","11"],["81","198","121"],["729","2673","3267","1331"]],"row_sums_preview":["1","20","400","8000","160000","3200000","64000000","1280000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-4e096b5929fd3f2e","steps":["reverse"],"edges":["e-381fdb511447f5c3"],"text":"A038323 \u2192 reverse"},"headline":"A038323 \u2192 reverse","chain":null}},{"id":"l-ee4f0ae275a32b06","kind":"fingerprint_related","node_a_id":"n-cfc5b48d32898a3e","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-cfc5b48d32898a3e","other":{"id":"n-cfc5b48d32898a3e","name":"Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*11^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["81","198","121"],["729","2673","3267","1331"],["6561","32076","58806","47916","14641"]],"card_rows":[["81","198","121"],["729","2673","3267","1331"],["6561","32076","58806","47916","14641"],["59049","360855","882090","1078110","658845","161051"]],"row_sums_preview":["400","8000","160000","3200000","64000000","1280000000","25600000000","512000000000"],"regions":["(-inf, 0)","(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-cfc5b48d32898a3e","steps":[],"edges":[],"text":"A038301"},"headline":"Triangle whose (i,j)-th entry is binomial(i,j)*9^(i-j)*11^j.","chain":null}},{"id":"l-fd3d89f73cb1ea93","kind":"fingerprint_related","node_a_id":"n-8156764a6e294c62","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-8156764a6e294c62","other":{"id":"n-8156764a6e294c62","name":"reversal of basis_map_A013609 of Triangle whose (i,j)-th entry is binomial(i,j)*7^(i-j)*11^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["22","18"],["484","792","324"]],"card_rows":[["1"],["22","18"],["484","792","324"],["10648","26136","21384","5832"]],"row_sums_preview":["1","40","1600","64000","2560000","102400000","4096000000","163840000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-b7cf68162d40a956","steps":["basis A013609","reverse"],"edges":["e-59f75239fe41171d","e-78c6f1d51c77ef97"],"text":"A038277 \u2192 basis A013609 \u2192 reverse"},"headline":"A038277 \u2192 basis A013609 \u2192 reverse","chain":null}},{"id":"l-febaa8057cd9aee5","kind":"fingerprint_related","node_a_id":"n-4e096b5929fd3f2e","node_b_id":"n-521827c5e15e2360","fingerprint":"f6-6bae7ffb6b8d3725","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-6bae7ffb6b8d3725"},"other_id":"n-4e096b5929fd3f2e","other":{"id":"n-4e096b5929fd3f2e","name":"Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.","first_index":0,"fingerprint":"f6-6bae7ffb6b8d3725","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["11","9"],["121","198","81"]],"card_rows":[["1"],["11","9"],["121","198","81"],["1331","3267","2673","729"]],"row_sums_preview":["1","20","400","8000","160000","3200000","64000000","1280000000"],"regions":["(-inf, 0)","(-inf, 0]"],"region_exact":{},"oeis_ids":["A038323"],"derivation":{"root":"n-4e096b5929fd3f2e","steps":[],"edges":[],"text":"A038323"},"headline":"A038323: Triangle whose (i,j)-th entry is binomial(i,j)*11^(i-j)*9^j.","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:             484,              792,               324;\n  1:           10648,            26136,             21384,              5832;\n  2:          234256,           766656,            940896,            513216,            104976;\n  3:         5153632,         21083040,          34499520,          28226880,          11547360,           1889568;\n  4:       113379904,        556592256,        1138484160,        1241982720,         762125760,         249422976,          34012224;\n  5:      2494357888,      14285867904,       35065312128,       47816334720,       39122455680,       19205569152,        5237882496,         612220032;\n  6:     54875873536,     359187535872,     1028582489088,     1683134982144,     1721388049920,     1126726723584,      460933659648,      107750725632,       11019960576;\n  7:   1207269217792,    8889891512832,    29094190405632,    55543454410752,    68166966776832,    55772972817408,    30421621536768,    10667321837568,     2181952194048,     198359290368;\n  8:  26559922791424,  217308459202560,   800090236154880,  1745651424337920,  2499455448483840,  2454010803965952,  1673189184522240,   782270268088320,   240014741345280,   43639043880960,   3570467226624;\n  9: 584318301411328, 5258864712701952, 21513537461053440, 52805955586222080, 86409745504727040, 98978435759960064, 80982356530876416, 47327351219343360, 19361189135185920, 5280324309596160, 864053068843008, 64268410079232;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (22+18*x)*P(n-1,x) for n >= 1, with P(0,x) = 484 + 792*x + 324*x^2.","mathematica":"P[0, x_] := 484 + 792*x + 324*x^2;\nP[n_, x_] := P[n, x] = Expand[(22 + 18*x)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 484 + 792*x + 324*x^2; for(n = 1, N, my(i = n + 1); v[i] = (22 + 18*x)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-4397e742863fdbe2","steps":["basis A013610","basis A013609"],"edges":["e-c80be26a429cc3fc","e-9512493cef2d9dab"],"text":"A038305 \u2192 basis A013610 \u2192 basis A013609"},"headline":"A038305 \u2192 basis A013610 \u2192 basis A013609","chain":null}