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22000;\n","recurrence_sentence":"The row polynomials satisfy (n+(3*n^2-n)*x+n^3*x^2)*P(n,x) = (n+3+(3*n^2+12*n+9)*x+(n^3+8*n^2+18*n+9)*x^2+(n^3+5*n^2+7*n+3)*x^3)*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[((n + 3 + (3*n^2 + 12*n + 9)*x + (n^3 + 8*n^2 + 18*n + 9)*x^2 + (n^3 + 5*n^2 + 7*n + 3)*x^3)*P[n - 1, x])/(n + (3*n^2 - n)*x + n^3*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] = ((n + 3 + (3*n^2 + 12*n + 9)*x + (n^3 + 8*n^2 + 18*n + 9)*x^2 + (n^3 + 5*n^2 + 7*n + 3)*x^3)*v[i - 1])/(n + (3*n^2 - n)*x + n^3*x^2)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, 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