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  134238060,   3247695;\n  9: 1396484375, 94569191145, 747698866200, 1666891865925, 1476369469575, 612282766095, 128417709420, 13820024790, 717740595, 14073345;\n","recurrence_sentence":"The row polynomials satisfy n*P(n,x) = (5*n+20+(3*n+12)*x)*P(n-1,x) + (3*n+12)*x*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[((5*n + 20 + (3*n + 12)*x)*P[n - 1, x] + (3*n + 12)*x*D[P[n - 1, x], x])/(n)]];\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] = ((5*n + 20 + (3*n + 12)*x)*v[i - 1] + (3*n + 12)*x*deriv(v[i - 1], x))/(n)); 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-79986ab5023c2764","steps":["basis A013610","basis A008277"],"edges":["e-0c010b1c5e20b0cb","e-64fa53535d8c2fa3"],"text":"A178821 \u2192 basis A013610 \u2192 basis A008277"},"headline":"A178821 \u2192 basis A013610 \u2192 basis A008277","chain":null}