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(4*n-2+(8*n-4)*x+16*n*x^2)*P(n-2,x) + (5*n+7+(8*n+12)*x)*P(n-1,x) for n >= 3, with P(0,x) = 1, P(1,x) = 3 + 4*x, P(2,x) = 9 + 28*x + 16*x^2.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 3 + 4*x;\nP[2, x_] := 9 + 28*x + 16*x^2;\nP[n_, x_] := P[n, x] = Expand[Together[((16*n - 32)*x^2*P[n - 3, x] - (4*n - 2 + (8*n - 4)*x + 16*n*x^2)*P[n - 2, x] + (5*n + 7 + (8*n + 12)*x)*P[n - 1, x])/(n + 3)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 3 + 4*x; v[3] = 9 + 28*x + 16*x^2; for(n = 3, N, my(i = n + 1); v[i] = ((16*n - 32)*x^2*v[i - 3] - (4*n - 2 + (8*n - 4)*x + 16*n*x^2)*v[i - 2] + (5*n + 7 + (8*n + 12)*x)*v[i - 1])/(n + 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-a88a492d75692c65","steps":["basis A013611"],"edges":["e-5612f726ea654c82"],"text":"A119308 \u2192 basis A013611"},"headline":"A119308 \u2192 basis A013611","chain":null}