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135444234240, 842764124160, 2962842624000, 6399740067840, 8710757314560, 7313988648960, 3471287581440, 714256704000;\n","recurrence_sentence":"The row polynomials satisfy (4+(18*n-6)*x+9*n^2*x^2)*P(n,x) = (8*n+(36*n^2+36*n)*x+(18*n^3+90*n^2+54*n)*x^2+(27*n^3+54*n^2+27*n)*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 + (36*n^2 + 36*n)*x + (18*n^3 + 90*n^2 + 54*n)*x^2 + (27*n^3 + 54*n^2 + 27*n)*x^3)*P[n - 1, x])/(4 + (18*n - 6)*x + 9*n^2*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 + (36*n^2 + 36*n)*x + (18*n^3 + 90*n^2 + 54*n)*x^2 + (27*n^3 + 54*n^2 + 27*n)*x^3)*v[i - 1])/(4 + (18*n - 6)*x + 9*n^2*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-cb5d49e71e46f2ed","steps":["basis A013610","(\u03b8+1)\u00b2"],"edges":["e-542183e09dec6678","e-67a09a40c50ecfd0"],"text":"A196347 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2"},"headline":"A196347 \u2192 basis A013610 \u2192 (\u03b8+1)\u00b2","chain":null}