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384,       480,       120;\n  5:      3840,      5760,      2160,       120;\n  6:     46080,     80640,     40320,      5040;\n  7:    645120,   1290240,    806400,    161280,     5040;\n  8:  10321920,  23224320,  17418240,   4838400,   362880;\n  9: 185794560, 464486400, 406425600, 145152000, 18144000, 362880;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (2*n+n*x)*P(n-1,x) - (2*x+2*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[(2*n + n*x)*P[n - 1, x] - (2*x + 2*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] = (2*n + n*x)*v[i - 1] - (2*x + 2*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, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-90f6949024558b8d","steps":["basis A007318"],"edges":["e-26a3e60cc630357d"],"text":"A228955 \u2192 basis A007318"},"headline":"A228955 \u2192 basis A007318","chain":null}