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+ 762*x^2 + 1292*x^3 + 646*x^4;\nP[n_, x_] := P[n, x] = Expand[Together[((8*n^2 - 20*n + 12 + (72*n^2 - 180*n + 108)*x + (264*n^2 - 660*n + 396)*x^2 + (504*n^2 - 1260*n + 756)*x^3 + (528*n^2 - 1320*n + 792)*x^4 + (288*n^2 - 720*n + 432)*x^5 + (64*n^2 - 160*n + 96)*x^6)*P[n - 3, x] - (36*n^2 - 34*n + 12 + (36*n^2 - 94*n + 84)*x - (180*n^2 + 70*n - 228)*x^2 - (396*n^2 - 14*n - 300)*x^3 - (288*n^2 - 32*n - 192)*x^4 - (72*n^2 - 8*n - 48)*x^5)*P[n - 2, x] - (48*x + 288*x^2 + 672*x^3 + 768*x^4 + 432*x^5 + 96*x^6)*D[P[n - 2, x], x] + (30*n^2 - 11*n + 1 + (150*n^2 - 55*n + 5)*x + (270*n^2 - 99*n + 9)*x^2 + (210*n^2 - 77*n + 7)*x^3 + (60*n^2 - 22*n + 2)*x^4)*P[n - 1, x] - ((54*n - 48)*x + (216*n - 192)*x^2 + (324*n - 288)*x^3 + (216*n - 192)*x^4 + (54*n - 48)*x^5)*D[P[n - 1, x], x])/(2*n^2 + 3*n + 1 + (6*n^2 + 9*n + 3)*x + (6*n^2 + 9*n + 3)*x^2 + (2*n^2 + 3*n + 1)*x^3)]];\nTable[CoefficientList[P[n, x], x], {n, 1, 10}] // Flatten","pari":"P(N) = {my(v = vector(N)); v[1] = 1 + 14*x + 14*x^2; v[2] = 1 + 48*x + 138*x^2 + 92*x^3; v[3] = 1 + 116*x + 762*x^2 + 1292*x^3 + 646*x^4; for(n = 4, N, my(i = n); v[i] = ((8*n^2 - 20*n + 12 + (72*n^2 - 180*n + 108)*x + (264*n^2 - 660*n + 396)*x^2 + (504*n^2 - 1260*n + 756)*x^3 + (528*n^2 - 1320*n + 792)*x^4 + (288*n^2 - 720*n + 432)*x^5 + (64*n^2 - 160*n + 96)*x^6)*v[i - 3] - (36*n^2 - 34*n + 12 + (36*n^2 - 94*n + 84)*x - (180*n^2 + 70*n - 228)*x^2 - (396*n^2 - 14*n - 300)*x^3 - (288*n^2 - 32*n - 192)*x^4 - (72*n^2 - 8*n - 48)*x^5)*v[i - 2] - (48*x + 288*x^2 + 672*x^3 + 768*x^4 + 432*x^5 + 96*x^6)*deriv(v[i - 2], x) + (30*n^2 - 11*n + 1 + (150*n^2 - 55*n + 5)*x + (270*n^2 - 99*n + 9)*x^2 + (210*n^2 - 77*n + 7)*x^3 + (60*n^2 - 22*n + 2)*x^4)*v[i - 1] - ((54*n - 48)*x + (216*n - 192)*x^2 + (324*n - 288)*x^3 + (216*n - 192)*x^4 + (54*n - 48)*x^5)*deriv(v[i - 1], x))/(2*n^2 + 3*n + 1 + (6*n^2 + 9*n + 3)*x + (6*n^2 + 9*n + 3)*x^2 + (2*n^2 + 3*n + 1)*x^3)); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i, v[i])))};\nT(10)","reading":{"first_row":1,"offset":1,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-f7935c36a3c0ec8c","steps":["\u2299 C(n+1,k) (shift +2)","x \u21a6 x/(x+1)"],"edges":["e-dbc1a9d96bc2026c","e-ddbb8c4f51a256ae"],"text":"A086645 \u2192 \u2299 C(n+1,k) (shift +2) \u2192 x \u21a6 x/(x+1)"},"headline":"A086645 \u2192 \u2299 C(n+1,k) (shift +2) \u2192 x \u21a6 x/(x+1)","chain":null}