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A013609","chain":null}},{"id":"l-fd916cce828a7f9d","kind":"fingerprint_related","node_a_id":"n-0f5fb19aff15410b","node_b_id":"n-c199d54e67c0f665","fingerprint":"f6-f06e51c139cfae05","oeis_id":null,"in_catalog":null,"target":null,"row_alignment":null,"rows_matched":null,"oeis_nonn":null,"details":{"fingerprint":"f6-f06e51c139cfae05"},"other_id":"n-0f5fb19aff15410b","other":{"id":"n-0f5fb19aff15410b","name":"basis_map_A013610 of Twice Pascal's triangle A007318: T(n,k) = 2*C(n,k).","first_index":0,"fingerprint":"f6-f06e51c139cfae05","polytool_family":null,"degree_pattern":"affine","palindromic":0,"gamma_positive":0,"nonnegative":1,"rr_by_factors":1,"preview_rows":[["2"],["4","6"],["8","24","18"]],"card_rows":[["2"],["4","6"],["8","24","18"],["16","72","108","54"]],"row_sums_preview":["2","10","50","250","1250","6250","31250","156250"],"regions":["(-inf, 0]","[-1, 0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-089a9b4f824a1c20","steps":["basis A013610"],"edges":["e-28b777b3c0b25332"],"text":"A028326 \u2192 basis A013610"},"headline":"A028326 \u2192 basis A013610","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:      1;\n  1:      6,       9;\n  2:     28,      84,       63;\n  3:    120,     540,      810,       405;\n  4:    496,    2976,     6696,      6696,      2511;\n  5:   2016,   15120,    45360,     68040,     51030,     15309;\n  6:   8128,   73152,   274320,    548640,    617220,    370332,     92583;\n  7:  32640,  342720,  1542240,   3855600,   5783400,   5205060,   2602530,    557685;\n  8: 130816, 1569792,  8241408,  24724224,  46357920,  55629504,  41722128,  17880912,   3352671;\n  9: 523776, 7070976, 42425856, 148490496, 334103616, 501155424, 501155424, 322171344, 120814254, 20135709;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = -(8+24*x+18*x^2)*P(n-2,x) + (6+9*x)*P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 6 + 9*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 6 + 9*x;\nP[n_, x_] := P[n, x] = Expand[-(8 + 24*x + 18*x^2)*P[n - 2, x] + (6 + 9*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; v[2] = 6 + 9*x; for(n = 2, N, my(i = n + 1); v[i] = -(8 + 24*x + 18*x^2)*v[i - 2] + (6 + 9*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-8d96419786c3ee2a","steps":["basis A013610"],"edges":["e-3119ad9ee9222212"],"text":"A134346 \u2192 basis A013610"},"headline":"A134346 \u2192 basis A013610","chain":null}