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D","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:           132,            72;\n  1:          2178,          2376,            648;\n  2:         31944,         52272,          28512,           5184;\n  3:        439230,        958320,         784080,         285120,          38880;\n  4:       5797836,      15812280,       17249760,        9408960,        2566080,         279936;\n  5:      74405562,     243509112,      332057880,      241496640,       98794080,       21555072,       1959552;\n  6:     935384208,    3571466976,     5844218688,     5312926080,     2897959680,      948423168,     172440576,      13436928;\n  7:   11575379574,   50510747232,    96429608352,   105195936384,    71724502080,    31297964544,    8535808512,    1330255872,     90699264;\n  8:  141476861460,  694522774440,  1515322416960,  1928592167040,  1577939045760,   860694024960,  312979645440,   73164072960,   9976919040,   604661760;\n  9: 1711870023666, 9337472856360, 22919251556520, 33337093173120, 31821770756160, 20828795404032, 9467634274560, 2950950942720, 603603601920, 73164072960, 3990767616;\n","recurrence_sentence":"The row polynomials satisfy (n+1)*P(n,x) = (11*n+22+(6*n+12)*x)*P(n-1,x) for n >= 1, with P(0,x) = 132 + 72*x.","mathematica":"P[0, x_] := 132 + 72*x;\nP[n_, x_] := P[n, x] = Expand[Together[((11*n + 22 + (6*n + 12)*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] = 132 + 72*x; for(n = 1, N, my(i = n + 1); v[i] = ((11*n + 22 + (6*n + 12)*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-1f2dec04776afb2b","steps":["D"],"edges":["e-ec5ce3b79dc5f6c1"],"text":"A038320 \u2192 D"},"headline":"A038320 \u2192 D","chain":null}