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    120;\n  5: 1,   62,   540,   1560,    1800,      720;\n  6: 1,  126,  1806,   8400,   16800,    15120,     5040;\n  7: 1,  254,  5796,  40824,  126000,   191520,   141120,    40320;\n  8: 1,  510, 18150, 186480,  834120,  1905120,  2328480,  1451520,   362880;\n  9: 1, 1022, 55980, 818520, 5103000, 16435440, 29635200, 30240000, 16329600, 3628800;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (1+2*x)*P(n-1,x) + (x+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[(1 + 2*x)*P[n - 1, x] + (x + x^2)*D[P[n - 1, x], x]];\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] = (1 + 2*x)*v[i - 1] + (x + x^2)*deriv(v[i - 1], x)); 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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