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   1;\n   6:   243,   891,   1323,   1035,    465,    121,    17,     1;\n   7:   729,  2916,   4860,   4428,   2430,    828,   172,    20,    1;\n   8:  2187,  9477,  17496,  18144,  11718,   4914,  1344,   232,   23,   1;\n   9:  6561, 30618,  61965,  71928,  53298,  26460,  8946,  2040,  301,  26,  1;\n  10: 19683, 98415, 216513, 277749, 231822, 132678, 53298, 15066, 2943, 379, 29, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where (n-1)*P(n,x) = (n-1+(3*n-3)*x)*P(n-1,x) for n >= 2, with P(1,x) = 1 + 2*x + x^2.","mathematica":"P[1, x_] := 1 + 2*x + x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 1 + (3*n - 3)*x)*P[n - 1, x])/(n - 1)]];\nTable[Reverse[CoefficientList[P[n, x], x]], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1 + 2*x + x^2; for(n = 2, N, my(i = n); v[i] = ((n - 1 + (3*n - 3)*x)*v[i - 1])/(n - 1)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = Vecrev(c); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, 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