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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:     3,      8,       3;\n  2:     9,     48,      66,       32,        5;\n  3:    27,    216,     513,      544,      285,        72,         7;\n  4:    81,    864,    2916,     4800,     4430,      2400,       756,       128,         9;\n  5:   243,   3240,   14175,    31680,    42150,     35664,     19670,      7040,      1575,       200,       11;\n  6:   729,  11664,   62694,   177120,   308475,    356832,    284452,    158592,     61695,     16400,     2838,      288,       13;\n  7:  2187,  40824,  260253,   889056,  1915515,   2816856,   2950437,   2251904,   1264473,    521640,   156079,    32928,     4641,     392,     15;\n  8:  6561, 139968, 1032264,  4136832, 10625580,  18978624,  24678360,  23999232,  17720406,   9999680,  4308920,  1405824,   341068,   59584,   7080,   512,    17;\n  9: 19683, 472392, 3956283, 18195840, 54281340, 114143904, 177477804, 210117888, 192887082, 138755440, 78583626, 35019648, 12207468, 3288096, 670140, 99840, 10251, 648, 19;\n","recurrence_sentence":"The row polynomials satisfy (3+4*n*x+(2*n-1)*x^2)*P(n,x) = (9+(12*n+24)*x+(22*n+22)*x^2+(12*n+8)*x^3+(2*n+1)*x^4)*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[((9 + (12*n + 24)*x + (22*n + 22)*x^2 + (12*n + 8)*x^3 + (2*n + 1)*x^4)*P[n - 1, x])/(3 + 4*n*x + (2*n - 1)*x^2)]];\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] = ((9 + (12*n + 24)*x + (22*n + 22)*x^2 + (12*n + 8)*x^3 + (2*n + 1)*x^4)*v[i - 1])/(3 + 4*n*x + (2*n - 1)*x^2)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = 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