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   109831140,       13286025,        531441;\n  7:   170859375,    4415612049,    16808179752,    19378759869,     8866207350,     1785641760,     156243654,      4782969;\n  8:  2562890625,  107512423551,   594410440257,   965181532266,   626585413671,   186934371750,   26851587966,   1779264468,    43046721;\n  9: 38443359375, 2603364180849, 20583156340440, 45887318317485, 40642489887615, 16855331028039, 3535168915404, 380446920198, 19758444939, 387420489;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (15+9*x)*P(n-1,x) + 9*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[(15 + 9*x)*P[n - 1, x] + 9*x*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] = (15 + 9*x)*v[i - 1] + 9*x*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-8d88ef9de74b305f","steps":["basis A013610","basis A008277"],"edges":["e-b88e4ed4246b1dea","e-6d18cd4c455b7e00"],"text":"A038221 \u2192 basis A013610 \u2192 basis A008277"},"headline":"A038221 \u2192 basis A013610 \u2192 basis A008277","chain":null}