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 23,   8,   1;\n  7: 1,  9, 31,  55,  55,  31,   9,  1;\n  8: 1, 10, 40,  86, 110,  86,  40, 10,  1;\n  9: 1, 11, 50, 126, 196, 196, 126, 50, 11, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where (n-3)*P(n,x) = (n-3+(n-3)*x)*P(n-1,x) for n >= 4, with P(0,x) = 1, P(1,x) = 1 + x, P(2,x) = 1 + 2*x + x^2, P(3,x) = 1 + 5*x + 5*x^2 + x^3.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 + x;\nP[2, x_] := 1 + 2*x + x^2;\nP[3, x_] := 1 + 5*x + 5*x^2 + x^3;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 3 + (n - 3)*x)*P[n - 1, x])/(n - 3)]];\nTable[Reverse[PadRight[CoefficientList[P[n, x], x], n + 1]], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 1 + x; v[3] = 1 + 2*x + x^2; v[4] = 1 + 5*x + 5*x^2 + x^3; for(n = 4, N, my(i = n + 1); v[i] = ((n - 3 + (n - 3)*x)*v[i - 1])/(n - 3)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c = Vecrev(c); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, 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