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v[1] = 1; v[2] = 4*x; for(n = 2, N, my(i = n + 1); v[i] = (-((n^2 - 5*n - 3)*x^2 + (n^2 - n - 29)*x^3 - (6*n^2 - 42*n + 87)*x^4 - (14*n^2 - 82*n + 117)*x^5 - (11*n^2 - 59*n + 74)*x^6 - (3*n^2 - 15*n + 18)*x^7)*v[i - 2] + ((2*n - 6)*x^2 + (4*n - 8)*x^3 - (10*n - 46)*x^4 - (40*n - 144)*x^5 - (50*n - 166)*x^6 - (28*n - 88)*x^7 - (6*n - 18)*x^8)*deriv(v[i - 2], x) - (x^2 + 3*x^3 - 3*x^4 - 25*x^5 - 45*x^6 - 39*x^7 - 17*x^8 - 3*x^9)*deriv(deriv(v[i - 2], x), x) - (1 + (2*n - 2)*x + (4*n - 10)*x^2 - 8*x^3 - (4*n - 1)*x^4 - (2*n - 2)*x^5)*v[i - 1] + (2*x + 6*x^2 + 4*x^3 - 4*x^4 - 6*x^5 - 2*x^6)*deriv(v[i - 1], 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-e65f982fa1b436c5","steps":["(\u03b8+1)\u00b2","x \u21a6 x/(x+1)"],"edges":["e-61c911ef7d81056e","e-c7f4a8399df4c6a6"],"text":"A048993 \u2192 (\u03b8+1)\u00b2 \u2192 x \u21a6 x/(x+1)"},"headline":"A048993 \u2192 (\u03b8+1)\u00b2 \u2192 x \u21a6 x/(x+1)","chain":null}