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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:            1;\n  1:           19,            43;\n  2:          361,          1634,           1849;\n  3:         6859,         46569,         105393,           79507;\n  4:       130321,       1179748,        4004934,         6042532,          3418801;\n  5:      2476099,      28019015,      126822910,       287020270,        324786095,        147008443;\n  6:     47045881,     638833542,     3614452935,     10906770260,      18512807415,      16758962502,       6321363049;\n  7:    893871739,   14160810181,    96144448071,    362650111145,     820734462065,    1114471006383,     840741285517,     271818611107;\n  8:  16983563041,  307491878216,  2435659351132,  11024563378808,   31187909558470,   56466530990072,   63896337699292,   41316428888264,   11688200277601;\n  9: 322687697779, 6572638896867, 59499678434796, 314200056296028, 1066626506899674, 2413944199825578, 3642091248859644, 3532554669946572, 1998682247469771, 502592611936843;\n","recurrence_sentence":"The row polynomials satisfy (1+x)*P(n,x) = (19+62*x+43*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((19 + 62*x + 43*x^2)*P[n - 1, x])/(1 + x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = ((19 + 62*x + 43*x^2)*v[i - 1])/(1 + x)); 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-2f02b2035f8f4541","steps":["basis A013610","x \u21a6 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