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Triangle by columns, (2^k, 0, 0, 0, ...).","first_index":0,"fingerprint":"f6-03d7b8417365c509","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["2","8"],["4","32","64"]],"card_rows":[["1"],["2","8"],["4","32","64"],["8","96","384","512"]],"row_sums_preview":["1","10","100","1000","10000","100000","1000000","10000000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-ae7910bbe46f8a41","steps":["basis A013611"],"edges":["e-d7d2422771947afc"],"text":"A130123 \u2192 basis A013611"},"headline":"A130123 \u2192 basis A013611","chain":null}},{"id":"l-ecc4ea45e06a5a79","kind":"fingerprint_related","node_a_id":"n-6e0864853f49fb26","node_b_id":"n-872d1ad8224c1da6","fingerprint":"f6-03d7b8417365c509","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-03d7b8417365c509"},"other_id":"n-6e0864853f49fb26","other":{"id":"n-6e0864853f49fb26","name":"basis_map_A013611 of basis-map coefficients of Triangle of coefficients in expansion of x^n in terms of Laguerre polynomials L_n(x).","first_index":1,"fingerprint":"f6-03d7b8417365c509","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":0,"rr_by_factors":1,"preview_rows":[["1"],["-1","-4"],["2","16","32"]],"card_rows":[["1"],["-1","-4"],["2","16","32"],["-6","-72","-288","-384"]],"row_sums_preview":["1","-5","50","-750","15000","-375000","11250000","-393750000"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-cf1765de6ac2bd4b","steps":["basis A013611"],"edges":["e-e262ea1acc16711f"],"text":"basis-map coefficients of A021012 \u2192 basis A013611"},"headline":"basis-map coefficients of A021012 \u2192 basis A013611","chain":null}},{"id":"l-fc60f68cc5e9dd7e","kind":"fingerprint_related","node_a_id":"n-ef5c9478e7d83dab","node_b_id":"n-872d1ad8224c1da6","fingerprint":"f6-03d7b8417365c509","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-03d7b8417365c509"},"other_id":"n-ef5c9478e7d83dab","other":{"id":"n-ef5c9478e7d83dab","name":"derivative of Triangle whose (i,j)-th entry is binomial(i,j)*4^(i-j).","first_index":0,"fingerprint":"f6-03d7b8417365c509","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[[],["1"],["8","2"]],"card_rows":[["1"],["8","2"],["48","24","3"],["256","192","48","4"]],"row_sums_preview":["0","1","10","75","500","3125","18750","109375"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-3dcaebc50e901d48","steps":["D"],"edges":["e-62aaaa59f91d42c1"],"text":"A038231 \u2192 D"},"headline":"A038231 \u2192 D","chain":null}},{"id":"l-fcdc1a680514534f","kind":"oeis_match","node_a_id":"n-872d1ad8224c1da6","node_b_id":null,"fingerprint":null,"oeis_id":"A052562","in_catalog":0,"target":"row_sums","row_alignment":null,"rows_matched":null,"oeis_nonn":1,"details":{"alignment":{"first_row":0,"low_zeros_dropped":false,"oeis_offset":0,"oeis_term_position":0,"target":"row_sums","terms_compared":15},"in_catalog":false,"oeis_id":"A052562","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A052562","relation":"match_row_sums"}],"bfiles":[{"node_id":"n-872d1ad8224c1da6","oeis_id":"A052562","target":"row_sums","oeis_offset":0,"first_row":0,"rows_used":200,"terms_matched":15,"oeis_terms_agreeing":16,"oeis_terms_available":16,"term_count":200,"raw_size":47967}],"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:      1;\n  1:      1,        4;\n  2:      2,       16,        32;\n  3:      6,       72,       288,        384;\n  4:     24,      384,      2304,       6144,        6144;\n  5:    120,     2400,     19200,      76800,      153600,      122880;\n  6:    720,    17280,    172800,     921600,     2764800,     4423680,      2949120;\n  7:   5040,   141120,   1693440,   11289600,    45158400,   108380160,    144506880,     82575360;\n  8:  40320,  1290240,  18063360,  144506880,   722534400,  2312110080,   4624220160,   5284823040,   2642411520;\n  9: 362880, 13063680, 209018880, 1950842880, 11705057280, 46820229120, 124853944320, 214035333120, 214035333120, 95126814720;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (n+4*n*x)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(n + 4*n*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] = 1; for(n = 1, N, my(i = n + 1); v[i] = (n + 4*n*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-fbb4b9430d9de872","steps":["basis A013611"],"edges":["e-d759043f254c4b9e"],"text":"A136572 \u2192 basis A013611"},"headline":"A136572 \u2192 basis A013611","chain":null}
