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(4*n+(18*n^2-6*n)*x+9*n^3*x^2)*P(n,x) = (8*n+24+(36*n^2+144*n+108)*x+(18*n^3+144*n^2+324*n+162)*x^2+(27*n^3+135*n^2+189*n+81)*x^3)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((8*n + 24 + (36*n^2 + 144*n + 108)*x + (18*n^3 + 144*n^2 + 324*n + 162)*x^2 + (27*n^3 + 135*n^2 + 189*n + 81)*x^3)*P[n - 1, x])/(4*n + (18*n^2 - 6*n)*x + 9*n^3*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] = ((8*n + 24 + (36*n^2 + 144*n + 108)*x + (18*n^3 + 144*n^2 + 324*n + 162)*x^2 + (27*n^3 + 135*n^2 + 189*n + 81)*x^3)*v[i - 1])/(4*n + (18*n^2 - 6*n)*x + 9*n^3*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-a820c1859f68e71c","steps":["basis A013610","(\u03b8+1)\u00b2"],"edges":["e-24fdbe8219e7135e","e-c2754db8ca3fb9e2"],"text":"A178820 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2"},"headline":"A178820 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2","chain":null}