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(48*n-124+(64*n^2-320*n+492)*x+(160*n-408)*x^2+64*x^3)*P(n-1,x) + ((32*n-88)*x-(32*n-152)*x^2-64*x^3)*d/dx P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 4 + 2*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 4 + 2*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(80*n - 140 + (128*n^2 - 640*n + 888)*x + (256*n^3 - 1856*n^2 + 4464*n - 3884)*x^2 + (768*n^2 - 3712*n + 4272)*x^3 + (512*n - 896)*x^4)*P[n - 2, x] - ((64*n - 112)*x + (256*n^2 - 1216*n + 1472)*x^2 - (256*n^2 - 1920*n + 3216)*x^3 - (768*n - 2368)*x^4 - 512*x^5)*D[P[n - 2, x], x] + (48*n - 124 + (64*n^2 - 320*n + 492)*x + (160*n - 408)*x^2 + 64*x^3)*P[n - 1, x] + ((32*n - 88)*x - (32*n - 152)*x^2 - 64*x^3)*D[P[n - 1, x], x])/(4*n - 11 + 8*x)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 4 + 2*x; for(n = 2, N, my(i = n + 1); v[i] = (-(80*n - 140 + (128*n^2 - 640*n + 888)*x + (256*n^3 - 1856*n^2 + 4464*n - 3884)*x^2 + (768*n^2 - 3712*n + 4272)*x^3 + (512*n - 896)*x^4)*v[i - 2] - ((64*n - 112)*x + (256*n^2 - 1216*n + 1472)*x^2 - (256*n^2 - 1920*n + 3216)*x^3 - (768*n - 2368)*x^4 - 512*x^5)*deriv(v[i - 2], x) + (48*n - 124 + (64*n^2 - 320*n + 492)*x + (160*n - 408)*x^2 + 64*x^3)*v[i - 1] + ((32*n - 88)*x - (32*n - 152)*x^2 - 64*x^3)*deriv(v[i - 1], x))/(4*n - 11 + 8*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-fb16da45c5e69d3d","steps":["D+1"],"edges":["e-8d42a4675fe7dade"],"text":"A257618 \u2192 D+1"},"headline":"A257618 \u2192 D+1","chain":null}