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70, 154, 154,  70,  14,   1;\n  8: 1, 16,  96, 272, 384, 272,  96,  16,  1;\n  9: 1, 18, 126, 438, 810, 810, 438, 126, 18, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where (n-2)*P(n,x) = (n-2+(n-2)*x)*P(n-1,x) + (n-2)*x*P(n-2,x) for n >= 3, with P(0,x) = 1, P(1,x) = 1 + x, P(2,x) = 1 + 4*x + x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 + x;\nP[2, x_] := 1 + 4*x + x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((n - 2 + (n - 2)*x)*P[n - 1, x] + (n - 2)*x*P[n - 2, x])/(n - 2)]];\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 + 4*x + x^2; for(n = 3, N, my(i = n + 1); v[i] = ((n - 2 + (n - 2)*x)*v[i - 1] + (n - 2)*x*v[i - 2])/(n - 2)); 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, row(i - 1, 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