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13)*x^4 + (n^2 - 3*n + 2)*x^5)*P[n - 1, x] + ((2*n + 7)*x + (6*n + 32)*x^2 + (4*n + 58)*x^3 - (4*n - 52)*x^4 - (6*n - 23)*x^5 - (2*n - 4)*x^6)*D[P[n - 1, x], x] + (x^2 + 5*x^3 + 10*x^4 + 10*x^5 + 5*x^6 + x^7)*D[P[n - 1, x], {x, 2}])/(1 + 2*x + 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] = ((n^2 + 6*n + 9 + (n^2 + 13*n + 35)*x - (2*n^2 - 52)*x^2 - (2*n^2 + 18*n - 37)*x^3 + (n^2 - 14*n + 13)*x^4 + (n^2 - 3*n + 2)*x^5)*v[i - 1] + ((2*n + 7)*x + (6*n + 32)*x^2 + (4*n + 58)*x^3 - (4*n - 52)*x^4 - (6*n - 23)*x^5 - (2*n - 4)*x^6)*deriv(v[i - 1], x) + (x^2 + 5*x^3 + 10*x^4 + 10*x^5 + 5*x^6 + x^7)*deriv(deriv(v[i - 1], x), x))/(1 + 2*x + 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-ee73bfb592710e97","steps":["x \u21a6 x/(x+1)"],"edges":["e-ad14854f4686feac"],"text":"A371081 \u2192 x \u21a6 x/(x+1)"},"headline":"A371081 \u2192 x \u21a6 x/(x+1)","chain":null}