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7, 48, 135,  200,  165,   72,   13;\n  7:  8, 63, 210,  385,  420,  273,   98,  15;\n  8:  9, 80, 308,  672,  910,  784,  420, 128,  17;\n  9: 10, 99, 432, 1092, 1764, 1890, 1344, 612, 162, 19;\n","recurrence_sentence":"Row n lists the coefficients of P(n,x) in descending powers of x, where (2*n-1)*P(n,x) = (2*n+1+(4*n-2)*x+(n-1)*x^2)*P(n-1,x) - (2*x+3*x^2+x^3)*d/dx 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[((2*n + 1 + (4*n - 2)*x + (n - 1)*x^2)*P[n - 1, x] - (2*x + 3*x^2 + x^3)*D[P[n - 1, x], x])/(2*n - 1)]];\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; for(n = 1, N, my(i = n + 1); v[i] = ((2*n + 1 + (4*n - 2)*x + (n - 1)*x^2)*v[i - 1] - (2*x + 3*x^2 + x^3)*deriv(v[i - 1], x))/(2*n - 1)); 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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