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4,   64,   216,   256,    100;\n  5:  8,  160,   720,  1280,   1000,    288;\n  6:  8,  192,  1080,  2560,   3000,   1728,    392;\n  7: 16,  448,  3024,  8960,  14000,  12096,   5488,  1024;\n  8: 16,  512,  4032, 14336,  28000,  32256,  21952,  8192,  1296;\n  9: 32, 1152, 10368, 43008, 100800, 145152, 131712, 73728, 23328, 3200;\n","recurrence_sentence":"The row polynomials satisfy (1+(3*n-4)*x+(n^2-2*n+1)*x^2)*P(n,x) = (2+(6*n+8)*x+(2*n^2+16*n+12)*x^2+(4*n^2+14*n+8)*x^3+(2*n^2+4*n+2)*x^4)*P(n-2,x) for n >= 2, with P(0,x) = 1, P(1,x) = 2 + 8*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 2 + 8*x;\nP[n_, x_] := P[n, x] = Expand[Together[((2 + (6*n + 8)*x + (2*n^2 + 16*n + 12)*x^2 + (4*n^2 + 14*n + 8)*x^3 + (2*n^2 + 4*n + 2)*x^4)*P[n - 2, x])/(1 + (3*n - 4)*x + (n^2 - 2*n + 1)*x^2)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 2 + 8*x; for(n = 2, N, my(i = n + 1); v[i] = ((2 + (6*n + 8)*x + (2*n^2 + 16*n + 12)*x^2 + (4*n^2 + 14*n + 8)*x^3 + (2*n^2 + 4*n + 2)*x^4)*v[i - 2])/(1 + (3*n - 4)*x + (n^2 - 2*n + 1)*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-a624e5aba8e1c39e","steps":["(\u03b8+1)\u00b2"],"edges":["e-064e625d7496a635"],"text":"A135838 \u2192 (\u03b8+1)\u00b2"},"headline":"A135838 \u2192 (\u03b8+1)\u00b2","chain":null}