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350*n + 284)*x^3 - (100*n^2 - 388*n + 291)*x^4 - (64*n^2 - 216*n + 152)*x^5 - (16*n^2 - 48*n + 32)*x^6)*P[n - 1, x] + (2 - (8*n - 40)*x - (64*n - 228)*x^2 - (208*n - 616)*x^3 - (352*n - 914)*x^4 - (328*n - 768)*x^5 - (160*n - 344)*x^6 - (32*n - 64)*x^7)*D[P[n - 1, x], x] + (4*x + 36*x^2 + 136*x^3 + 280*x^4 + 340*x^5 + 244*x^6 + 96*x^7 + 16*x^8)*D[P[n - 1, x], {x, 2}])/(1 + 3*x + 3*x^2 + x^3)]];\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] = (-(2*n - 3 - (4*n^2 - 34*n + 36)*x - (28*n^2 - 162*n + 146)*x^2 - (76*n^2 - 350*n + 284)*x^3 - (100*n^2 - 388*n + 291)*x^4 - (64*n^2 - 216*n + 152)*x^5 - (16*n^2 - 48*n + 32)*x^6)*v[i - 1] + (2 - (8*n - 40)*x - (64*n - 228)*x^2 - (208*n - 616)*x^3 - (352*n - 914)*x^4 - (328*n - 768)*x^5 - (160*n - 344)*x^6 - (32*n - 64)*x^7)*deriv(v[i - 1], x) + (4*x + 36*x^2 + 136*x^3 + 280*x^4 + 340*x^5 + 244*x^6 + 96*x^7 + 16*x^8)*deriv(deriv(v[i - 1], x), x))/(1 + 3*x + 3*x^2 + x^3)); 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-3338feb205e3b77f","steps":["x \u21a6 x/(x+1)"],"edges":["e-10d1b71ae1dabec3"],"text":"A151775 \u2192 x \u21a6 x/(x+1)"},"headline":"A151775 \u2192 x \u21a6 x/(x+1)","chain":null}