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32837805,     3127410;\n  8:  1833173,  26966412,  169266636,  588648060,  1228701474,  1549944396,  1115025912,   382794984,   31899582;\n  9: 10330173, 173674962, 1271699676, 5301960300, 13788295794, 22974522480, 24116083992, 14859405288, 4463041518, 330595668;\n","recurrence_sentence":"The row polynomials satisfy (27*n^3+81*n^2+48*n-12+(81*n+162)*x-(27*n+54)*x^2)*P(n,x) = (81*n^3+405*n^2+594*n+216+(162*n^3+810*n^2+1341*n+738)*x+(243*n+486)*x^2-(162*n+324)*x^3)*P(n-1,x) + (36*n^2+72*n+28+(162*n^2+324*n+162)*x+(162*n^2+324*n+252)*x^2-162*x^4)*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[((81*n^3 + 405*n^2 + 594*n + 216 + (162*n^3 + 810*n^2 + 1341*n + 738)*x + (243*n + 486)*x^2 - (162*n + 324)*x^3)*P[n - 1, x] + (36*n^2 + 72*n + 28 + (162*n^2 + 324*n + 162)*x + (162*n^2 + 324*n + 252)*x^2 - 162*x^4)*D[P[n - 1, x], x])/(27*n^3 + 81*n^2 + 48*n - 12 + (81*n + 162)*x - (27*n + 54)*x^2)]];\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] = ((81*n^3 + 405*n^2 + 594*n + 216 + (162*n^3 + 810*n^2 + 1341*n + 738)*x + (243*n + 486)*x^2 - (162*n + 324)*x^3)*v[i - 1] + (36*n^2 + 72*n + 28 + (162*n^2 + 324*n + 162)*x + (162*n^2 + 324*n + 252)*x^2 - 162*x^4)*deriv(v[i - 1], x))/(27*n^3 + 81*n^2 + 48*n - 12 + (81*n + 162)*x - (27*n + 54)*x^2)); 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-66e2c3448245b0b7","steps":["basis A013610","D+1"],"edges":["e-13974c051c6d411c","e-498fef8d1053424f"],"text":"A033282 \u2192 basis A013610 \u2192 D+1"},"headline":"A033282 \u2192 basis A013610 \u2192 D+1","chain":null}