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0]"}]}],"used_by":[],"used_by_total":0,"links":[],"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:         7,          4;\n  2:        84,        146,         84,          16;\n  3:       756,       2196,       2541,        1464,         420,          48;\n  4:      6048,      24624,      42840,       41284,       23800,        8208,        1568,         128;\n  5:     45360,     237600,     551880,      746040,      646835,      373020,      143080,       35200,        5040,         320;\n  6:    326592,    2091744,    6078240,    10577520,    12248460,     9909654,     5715948,     2350560,      675360,      129120,      14784,        768;\n  7:   2286144,   17309376,   60392304,   128562336,   186304860,   194077548,   149520217,    86256688,    37260972,    11903920,    2733808,     427392,     40768,      1792;\n  8:  15676416,  136982016,  557819136,  1404273024,  2444057280,  3115113120,  3003741552,  2231241992,  1287317808,   576872800,  199145408,   52010112,   9947392,   1315328,   107520,    4096;\n  9: 105815808, 1048080384, 4879284480, 14179878144, 28811129760, 43433578944, 50305900176, 45724352688, 33018844383, 19051813620, 8783569872, 3217302144, 924801696, 204236928, 33465600, 3833856, 274176, 9216;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (6*n+7*n*x+2*n*x^2)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 7 + 4*x.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 7 + 4*x;\nP[n_, x_] := P[n, x] = Expand[Together[((6*n + 7*n*x + 2*n*x^2)*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] = 7 + 4*x; for(n = 2, N, my(i = n + 1); v[i] = ((6*n + 7*n*x + 2*n*x^2)*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-eed4f744ce063213","steps":["basis A007318","D"],"edges":["e-6e97878f95ac8f6d","e-561980871c66264d"],"text":"A200536 \u2192 basis A007318 \u2192 D"},"headline":"A200536 \u2192 basis A007318 \u2192 D","chain":null}