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reverse","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:         0;\n  1:         3;\n  2:        42,        18;\n  3:       441,       378,        81;\n  4:      4116,      5292,      2268,       324;\n  5:     36015,     61740,     39690,     11340,      1215;\n  6:    302526,    648270,    555660,    238140,     51030,      4374;\n  7:   2470629,   6353046,   6806835,   3889620,   1250235,    214326,    15309;\n  8:  19765032,  59295096,  76236552,  54454680,  23337720,   6001128,   857304,   52488;\n  9: 155649627, 533655864, 800483796, 686128968, 367569090, 126023688, 27005076, 3306744, 177147;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (7*n+3*n*x)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 3.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 3;\nP[n_, x_] := P[n, x] = Expand[Together[((7*n + 3*n*x)*P[n - 1, x])/(n - 1)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 0; v[2] = 3; for(n = 2, N, my(i = n + 1); v[i] = ((7*n + 3*n*x)*v[i - 1])/(n - 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-22693abd431a71f2","steps":["basis A013610","D"],"edges":["e-b9cdb58d54bdc029","e-108da488069017c7"],"text":"A038255 \u2192 basis A013610 \u2192 D"},"headline":"A038255 \u2192 basis A013610 \u2192 D","chain":null}