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108,  128,   50;\n  5: 2, 40, 180,  320,  250,   72;\n  6: 2, 48, 270,  640,  750,  432,   98;\n  7: 2, 56, 378, 1120, 1750, 1512,  686,  128;\n  8: 2, 64, 504, 1792, 3500, 4032, 2744, 1024,  162;\n  9: 2, 72, 648, 2688, 6300, 9072, 8232, 4608, 1458, 200;\n","recurrence_sentence":"The row polynomials satisfy (1+(3*n-1)*x+n^2*x^2)*P(n,x) = (1+(3*n+3)*x+(n^2+5*n+3)*x^2+(n^2+2*n+1)*x^3)*P(n-1,x) for n >= 1, with P(0,x) = 2.","mathematica":"P[0, x_] := 2;\nP[n_, x_] := P[n, x] = Expand[Together[((1 + (3*n + 3)*x + (n^2 + 5*n + 3)*x^2 + (n^2 + 2*n + 1)*x^3)*P[n - 1, x])/(1 + (3*n - 1)*x + n^2*x^2)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 2; for(n = 1, N, my(i = n + 1); v[i] = ((1 + (3*n + 3)*x + (n^2 + 5*n + 3)*x^2 + (n^2 + 2*n + 1)*x^3)*v[i - 1])/(1 + (3*n - 1)*x + 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-089a9b4f824a1c20","steps":["(\u03b8+1)\u00b2"],"edges":["e-441c553de3723fe4"],"text":"A028326 \u2192 (\u03b8+1)\u00b2"},"headline":"A028326 \u2192 (\u03b8+1)\u00b2","chain":null}