{"id":"n-2ec4ee15f07899eb","revision":1,"first_index":0,"fingerprint":"f6-2327141074f67bdf","name":"one_plus_derivative of Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.","polytool_family":null,"interpretation":null,"rows_observed":15,"degree_pattern":"affine","degree_slope":1,"degree_intercept":0,"palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":true,"rows":[["1"],["3","3"],["0","12","6"],["0","0","30","10"],["0","0","0","60","15"],["0","0","0","0","105","21"],["0","0","0","0","0","168","28"],["0","0","0","0","0","0","252","36"],["0","0","0","0","0","0","0","360","45"],["0","0","0","0","0","0","0","0","495","55"],["0","0","0","0","0","0","0","0","0","660","66"],["0","0","0","0","0","0","0","0","0","0","858","78"],["0","0","0","0","0","0","0","0","0","0","0","1092","91"],["0","0","0","0","0","0","0","0","0","0","0","0","1365","105"],["0","0","0","0","0","0","0","0","0","0","0","0","0","1680","120"]],"degrees":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"row_sums":["1","6","18","40","75","126","196","288","405","550","726","936","1183","1470","1800"],"nonn":true,"definitions":[{"position":0,"source":"derived:one_plus_derivative","source_kind":"derived","equality_edge_id":null,"recurrence":{"first_index":0,"initial_polynomials":[["1"],["3","3"],["0","12","6"]],"recurrence":{"denominator":{"coeffs":[["-6","11","-6","1"],["11","-12","3","0"],["-6","3","0","0"],["1","0","0","0"]]},"terms":[{"coeff":{"coeffs":[["0","0","0","0","2","-3","1"],["0","0","0","2","-6","3","0"],["0","0","0","-3","3","0","0"],["0","0","0","1","0","0","0"]]},"deriv_order":0,"offset":3,"sign":"none"},{"coeff":{"coeffs":[["0","0","0","-9","12","-3"],["0","0","-9","24","-9","0"],["0","0","12","-9","0","0"],["0","0","-3","0","0","0"]]},"deriv_order":0,"offset":2,"sign":"none"},{"coeff":{"coeffs":[["0","0","18","-15","3"],["0","18","-30","9","0"],["0","-15","9","0","0"],["0","3","0","0","0"]]},"deriv_order":0,"offset":1,"sign":"none"}]},"schema":"polytool.recurrence.v1"}}],"properties":[{"id":161024,"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-28592ff7e93ff570"]},{"id":161025,"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-28592ff7e93ff570"]},{"id":161026,"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-28592ff7e93ff570"]}],"region_exact":{},"incoming_edges":[{"id":"e-28592ff7e93ff570","operation":{"index_shift":0,"operation":"preserver_image","operator":"{\"shape\":\"derivative_polynomial\",\"coefficients\":[{\"numerator\":[\"1\"],\"denominator\":[\"1\"]},{\"numerator\":[\"1\"],\"denominator\":[\"1\"]}]}"},"operation_detail":"derivative_polynomial, shift 0","conclusion_id":"n-2ec4ee15f07899eb","premise_count":1,"theorem":"Laguerre's theorem on differential operators: if phi is a real polynomial with only real roots, then phi(D) maps every real-rooted polynomial to a real-rooted polynomial or zero (write phi(D) = C D^j prod (1 + c_i D); D preserves real-rootedness by Rolle's theorem and p + c p' is real-rooted for every real c by Rolle's theorem applied to e^(x/c) p; Polya--Schur 1914); when the coefficients of phi have one sign, coefficients of one sign stay of one sign; applied to phi(n, .) for each n","lean_route":null,"lean_declarations":["RealRooted.splits_add_C_mul_derivative_all","RealRooted.splits_C_mul_add_derivative","Polynomial.Splits.derivative"],"certificate_hash":"d02bb62204c1d6d64cae91c13fffe2a53f8d3235ad7b03f573d756971afd1086","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-511a2225fa2191c9","role":"sequence","name":"Triangle read by rows: row n consists of n-1 zeros followed by n(n+1)/2.","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-1f3cd9d04c5e1a73","kind":"fingerprint_related","node_a_id":"n-bd4ec312ebef253e","node_b_id":"n-2ec4ee15f07899eb","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-bd4ec312ebef253e","other":{"id":"n-bd4ec312ebef253e","name":"one_plus_derivative of 3n + 1 preceded by n zeros.","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["4","4"],["0","14","7"]],"card_rows":[["1"],["4","4"],["0","14","7"],["0","0","30","10"]],"row_sums_preview":["1","8","21","40","65","96","133","176"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-39194b37db596ae8","steps":["reverse","D+1"],"edges":["e-e8da6a4618f02a9d","e-133ff869421f85a2"],"text":"A010054 \u2192 reverse \u2192 D+1"},"headline":"A010054 \u2192 reverse \u2192 D+1","chain":null}},{"id":"l-31d111c7d65611c6","kind":"fingerprint_related","node_a_id":"n-403f3ef85bba9ebc","node_b_id":"n-2ec4ee15f07899eb","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-403f3ef85bba9ebc","other":{"id":"n-403f3ef85bba9ebc","name":"one_plus_derivative of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals. shifted by x -> -x + 0","first_index":1,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":0,"rr_by_factors":1,"preview_rows":[["1"],["-1","-1"],["0","2","1"]],"card_rows":[["1"],["-1","-1"],["0","2","1"],["0","0","-3","-1"]],"row_sums_preview":["1","-2","3","-4","5","-6","7","-8"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-3cc7875cf81a5a84","steps":["D+1"],"edges":["e-dffa2a76d9a73ed0"],"text":"basis-map coefficients of A026729, shifted \u2192 D+1"},"headline":"basis-map coefficients of A026729, shifted \u2192 D+1","chain":null}},{"id":"l-56cb09120e71bea5","kind":"fingerprint_related","node_a_id":"n-2ec4ee15f07899eb","node_b_id":"n-941fc2b5950fdf03","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-941fc2b5950fdf03","other":{"id":"n-941fc2b5950fdf03","name":"one_plus_derivative of Triangle read by rows: row n consists of n zeros followed by n!.","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["1","1"],["0","4","2"]],"card_rows":[["1"],["1","1"],["0","4","2"],["0","0","18","6"]],"row_sums_preview":["1","2","6","24","120","720","5040","40320"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-fbb4b9430d9de872","steps":["D+1"],"edges":["e-3f0ee2ef76204334"],"text":"A136572 \u2192 D+1"},"headline":"A136572 \u2192 D+1","chain":null}},{"id":"l-71ccee831ae20dd9","kind":"fingerprint_related","node_a_id":"n-d16445f4fa1fddba","node_b_id":"n-2ec4ee15f07899eb","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-d16445f4fa1fddba","other":{"id":"n-d16445f4fa1fddba","name":"one_plus_derivative of Infinitesimal Pascal matrix: generator (lower triangular matrix representation) of the Pascal matrix, the classical operator xDx, iterated Laguerre transforms, associated matrices of the list partition transform and general Euler transformation for sequences.","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[[],["1"],["2","2"]],"card_rows":[["1"],["2","2"],["0","6","3"],["0","0","12","4"]],"row_sums_preview":["0","1","4","9","16","25","36","49"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-6fea5aff4f44fa54","steps":["D","D+1"],"edges":["e-12f4d751ee3d86a1","e-9e777fb0c714fbf5"],"text":"A023531 \u2192 D \u2192 D+1"},"headline":"A023531 \u2192 D \u2192 D+1","chain":null}},{"id":"l-748485d67ba9af14","kind":"fingerprint_related","node_a_id":"n-2ec4ee15f07899eb","node_b_id":"n-fc17ecb54217ecb0","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-fc17ecb54217ecb0","other":{"id":"n-fc17ecb54217ecb0","name":"one_plus_derivative of Triangle read by rows: n-th row is n^2 preceded by (n-1) zeros.","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["4","4"],["0","18","9"]],"card_rows":[["1"],["4","4"],["0","18","9"],["0","0","48","16"]],"row_sums_preview":["1","8","27","64","125","216","343","512"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-6fea5aff4f44fa54","steps":["(\u03b8+1)\u00b2","D+1"],"edges":["e-2da0845bd9c8c38c","e-d2b4dbb1c98c4e4a"],"text":"A023531 \u2192 (\u03b8+1)\u00b2 \u2192 D+1"},"headline":"A023531 \u2192 (\u03b8+1)\u00b2 \u2192 D+1","chain":null}},{"id":"l-93ec3e19e0f26a65","kind":"fingerprint_related","node_a_id":"n-df1048264f0e324d","node_b_id":"n-2ec4ee15f07899eb","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-df1048264f0e324d","other":{"id":"n-df1048264f0e324d","name":"one_plus_derivative of basis-map coefficients of Triangle read by rows: T(n,k) = binomial(k,n-k). shifted by x -> -x + 0","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":0,"rr_by_factors":1,"preview_rows":[["1"],["-1","-1"],["0","2","1"]],"card_rows":[["1"],["-1","-1"],["0","2","1"],["0","0","-3","-1"]],"row_sums_preview":["1","-2","3","-4","5","-6","7","-8"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-477d9807e1cbb785","steps":["D+1"],"edges":["e-806cb45b24538e1b"],"text":"basis-map coefficients of A030528, shifted \u2192 D+1"},"headline":"basis-map coefficients of A030528, shifted \u2192 D+1","chain":null}},{"id":"l-a4228397b612ed03","kind":"fingerprint_related","node_a_id":"n-b02759cc44b24b37","node_b_id":"n-2ec4ee15f07899eb","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-b02759cc44b24b37","other":{"id":"n-b02759cc44b24b37","name":"one_plus_derivative of basis-map coefficients of Square array of binomial coefficients T(n,k) = binomial(n,k), n >= 0, k >= 0, read by downward antidiagonals.","first_index":1,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["1","1"],["0","2","1"]],"card_rows":[["1"],["1","1"],["0","2","1"],["0","0","3","1"]],"row_sums_preview":["1","2","3","4","5","6","7","8"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-1bf99ad40f056d33","steps":["D+1"],"edges":["e-38c6c0f2ea6fe646"],"text":"basis-map coefficients of A026729 \u2192 D+1"},"headline":"basis-map coefficients of A026729 \u2192 D+1","chain":null}},{"id":"l-d28dbb728a93b763","kind":"fingerprint_related","node_a_id":"n-2ec4ee15f07899eb","node_b_id":"n-cbfe82ee301c996d","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-cbfe82ee301c996d","other":{"id":"n-cbfe82ee301c996d","name":"one_plus_derivative of Infinite lower triangular matrix with 2^k in the right diagonal and the rest zeros. Triangle, T(n,k), n zeros followed by the term 2^k. Triangle by columns, (2^k, 0, 0, 0, ...).","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["2","2"],["0","8","4"]],"card_rows":[["1"],["2","2"],["0","8","4"],["0","0","24","8"]],"row_sums_preview":["1","4","12","32","80","192","448","1024"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-ae7910bbe46f8a41","steps":["D+1"],"edges":["e-caef435f2360eea3"],"text":"A130123 \u2192 D+1"},"headline":"A130123 \u2192 D+1","chain":null}},{"id":"l-d87db5efe4c62d27","kind":"fingerprint_related","node_a_id":"n-2ec4ee15f07899eb","node_b_id":"n-00cbe48522a066a8","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-00cbe48522a066a8","other":{"id":"n-00cbe48522a066a8","name":"one_plus_derivative 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":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":0,"rr_by_factors":1,"preview_rows":[["1"],["-1","-1"],["0","4","2"]],"card_rows":[["1"],["-1","-1"],["0","4","2"],["0","0","-18","-6"]],"row_sums_preview":["1","-2","6","-24","120","-720","5040","-40320"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-cf1765de6ac2bd4b","steps":["D+1"],"edges":["e-224ed4e0bc1e1628"],"text":"basis-map coefficients of A021012 \u2192 D+1"},"headline":"basis-map coefficients of A021012 \u2192 D+1","chain":null}},{"id":"l-d951d36297e69d8a","kind":"fingerprint_related","node_a_id":"n-81d4142d81fa222d","node_b_id":"n-2ec4ee15f07899eb","fingerprint":"f6-2327141074f67bdf","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-2327141074f67bdf"},"other_id":"n-81d4142d81fa222d","other":{"id":"n-81d4142d81fa222d","name":"one_plus_derivative of a(n) = 1 if n is of the form m(m+3)/2, otherwise 0.","first_index":0,"fingerprint":"f6-2327141074f67bdf","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["1"],["1","1"],["0","2","1"]],"card_rows":[["1"],["1","1"],["0","2","1"],["0","0","3","1"]],"row_sums_preview":["1","2","3","4","5","6","7","8"],"regions":["(-inf, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-6fea5aff4f44fa54","steps":["D+1"],"edges":["e-63014276e02483f9"],"text":"A023531 \u2192 D+1"},"headline":"A023531 \u2192 D+1","chain":null}},{"id":"l-0dac22dfcebcae36","kind":"oeis_match","node_a_id":"n-2ec4ee15f07899eb","node_b_id":null,"fingerprint":null,"oeis_id":"A002411","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":1,"target":"row_sums","terms_compared":15},"in_catalog":false,"oeis_id":"A002411","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A002411","relation":"match_row_sums"}],"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: 1;\n  1: 3,  3;\n  2: 0, 12,  6;\n  3: 0,  0, 30, 10;\n  4: 0,  0,  0, 60,  15;\n  5: 0,  0,  0,  0, 105,  21;\n  6: 0,  0,  0,  0,   0, 168,  28;\n  7: 0,  0,  0,  0,   0,   0, 252,  36;\n  8: 0,  0,  0,  0,   0,   0,   0, 360,  45;\n  9: 0,  0,  0,  0,   0,   0,   0,   0, 495, 55;\n","recurrence_sentence":"The row polynomials satisfy (n^3-6*n^2+11*n-6+(3*n^2-12*n+11)*x+(3*n-6)*x^2+x^3)*P(n,x) = ((n^3-3*n^2+2*n)*x^3+(3*n^2-6*n+2)*x^4+(3*n-3)*x^5+x^6)*P(n-3,x) - ((3*n^3-12*n^2+9*n)*x^2+(9*n^2-24*n+9)*x^3+(9*n-12)*x^4+3*x^5)*P(n-2,x) + ((3*n^3-15*n^2+18*n)*x+(9*n^2-30*n+18)*x^2+(9*n-15)*x^3+3*x^4)*P(n-1,x) for n >= 3, with P(0,x) = 1, P(1,x) = 3 + 3*x, P(2,x) = 12*x + 6*x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3 + 3*x;\nP[2, x_] := 12*x + 6*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[(((n^3 - 3*n^2 + 2*n)*x^3 + (3*n^2 - 6*n + 2)*x^4 + (3*n - 3)*x^5 + x^6)*P[n - 3, x] - ((3*n^3 - 12*n^2 + 9*n)*x^2 + (9*n^2 - 24*n + 9)*x^3 + (9*n - 12)*x^4 + 3*x^5)*P[n - 2, x] + ((3*n^3 - 15*n^2 + 18*n)*x + (9*n^2 - 30*n + 18)*x^2 + (9*n - 15)*x^3 + 3*x^4)*P[n - 1, x])/(n^3 - 6*n^2 + 11*n - 6 + (3*n^2 - 12*n + 11)*x + (3*n - 6)*x^2 + x^3)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 3 + 3*x; v[3] = 12*x + 6*x^2; for(n = 3, N, my(i = n + 1); v[i] = (((n^3 - 3*n^2 + 2*n)*x^3 + (3*n^2 - 6*n + 2)*x^4 + (3*n - 3)*x^5 + x^6)*v[i - 3] - ((3*n^3 - 12*n^2 + 9*n)*x^2 + (9*n^2 - 24*n + 9)*x^3 + (9*n - 12)*x^4 + 3*x^5)*v[i - 2] + ((3*n^3 - 15*n^2 + 18*n)*x + (9*n^2 - 30*n + 18)*x^2 + (9*n - 15)*x^3 + 3*x^4)*v[i - 1])/(n^3 - 6*n^2 + 11*n - 6 + (3*n^2 - 12*n + 11)*x + (3*n - 6)*x^2 + x^3)); 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-39194b37db596ae8","steps":["reverse","D+1"],"edges":["e-9c0dd75b125bab92","e-28592ff7e93ff570"],"text":"A010054 \u2192 reverse \u2192 D+1"},"headline":"A010054 \u2192 reverse \u2192 D+1","chain":null}
