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1,  6,    3;\n  3: 1, 12,   18,     4;\n  4: 1, 20,   60,    40,     5;\n  5: 1, 30,  150,   200,    75,     6;\n  6: 1, 42,  315,   700,   525,   126,     7;\n  7: 1, 56,  588,  1960,  2450,  1176,   196,    8;\n  8: 1, 72, 1008,  4704,  8820,  7056,  2352,  288,   9;\n  9: 1, 90, 1620, 10080, 26460, 31752, 17640, 4320, 405, 10;\n","recurrence_sentence":"The row polynomials satisfy (n^2+n)*P(n,x) = (n^2+n+(3*n^2+n)*x)*P(n-1,x) + ((2*n+1)*x-(2*n+1)*x^2)*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[((n^2 + n + (3*n^2 + n)*x)*P[n - 1, x] + ((2*n + 1)*x - (2*n + 1)*x^2)*D[P[n - 1, x], x])/(n^2 + n)]];\nTable[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] = ((n^2 + n + (3*n^2 + n)*x)*v[i - 1] + ((2*n + 1)*x - (2*n + 1)*x^2)*deriv(v[i - 1], x))/(n^2 + n)); v};\nrow(n, p) = {my(c = Vecrev(p)); c = concat(c, vector(n + 1 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