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25,  100,  100,    25,     1;\n  6: 1, 36,  225,  400,   225,    36,    1;\n  7: 1, 49,  441, 1225,  1225,   441,   49,    1;\n  8: 1, 64,  784, 3136,  4900,  3136,  784,   64,  1;\n  9: 1, 81, 1296, 7056, 15876, 15876, 7056, 1296, 81, 1;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where n*P(n,x) = (2*n-1+(2*n-1)*x)*P(n-1,x) - (n-1-(2*n-2)*x+(n-1)*x^2)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 1 + x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 1 + x;\nP[n_, x_] := P[n, x] = Expand[Together[((2*n - 1 + (2*n - 1)*x)*P[n - 1, x] - (n - 1 - (2*n - 2)*x + (n - 1)*x^2)*P[n - 2, x])/(n)]];\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; for(n = 2, N, my(i = n + 1); v[i] = ((2*n - 1 + (2*n - 1)*x)*v[i - 1] - (n - 1 - (2*n - 2)*x + (n - 1)*x^2)*v[i - 2])/(n)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 - #c)); c = 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