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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:        14,         16;\n  2:       168,        584,         672,          256;\n  3:      1512,       8784,       20328,        23424,        13440,          3072;\n  4:     12096,      98496,      342720,       660544,       761600,        525312,        200704,          32768;\n  5:     90720,     950400,     4415040,     11936640,     20698720,      23873280,      18314240,        9011200,        2580480,         327680;\n  6:    653184,    8366976,    48625920,    169240320,    391950720,     634217856,     731641344,      601743360,      345784320,      132218880,       30277632,        3145728;\n  7:   4572288,   69237504,   483138432,   2056997376,   5961755520,   12420963072,   19138587776,    22081712128,    19077617664,    12189614080,     5598838784,     1750597632,     333971456,      29360128;\n  8:  31352832,  547928064,  4462553088,  22468368384,  78209832960,  199367239680,  384478918656,   571197949952,   659106717696,   590717747200,   407849795584,   213033418752,   81489035264,   21550333952,    3523215360,    268435456;\n  9: 211631616, 4192321536, 39034275840, 226878050304, 921956152320, 2779749052416, 6439155222528, 11705434288128, 16905648324096, 19509057146880, 17988751097856, 13178069581824, 7575975493632, 3346217828352, 1096600780800, 251255586816, 35936796672, 2415919104;\n","recurrence_sentence":"The row polynomials satisfy (n-1)*P(n,x) = (6*n+14*n*x+8*n*x^2)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 14 + 16*x.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 14 + 16*x;\nP[n_, x_] := P[n, x] = Expand[Together[((6*n + 14*n*x + 8*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] = 14 + 16*x; for(n = 2, N, my(i = n + 1); v[i] = ((6*n + 14*n*x + 8*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 A013609","D"],"edges":["e-185113cbc4b6c77b","e-ca6b7de726b3a729"],"text":"A200536 \u2192 basis A013609 \u2192 D"},"headline":"A200536 \u2192 basis A013609 \u2192 D","chain":null}