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 4:  25,  400,  1350,   1600,    625;\n  5:  36,  720,  3240,   5760,   4500,   1296;\n  6:  49, 1176,  6615,  15680,  18375,  10584,   2401;\n  7:  64, 1792, 12096,  35840,  56000,  48384,  21952,   4096;\n  8:  81, 2592, 20412,  72576, 141750, 163296, 111132,  41472,  6561;\n  9: 100, 3600, 32400, 134400, 315000, 453600, 411600, 230400, 72900, 10000;\n","recurrence_sentence":"The row polynomials satisfy (n^4-2*n^3+n^2)*P(n,x) = -(n^4+2*n^3+n^2+(4*n^4+8*n^3+4*n^2)*x-(9*n^4+18*n^3+9*n^2)*x^2)*P(n-2,x) + ((4*n^4+8*n^3+4*n^2)*x^2+(4*n^4+8*n^3+4*n^2)*x^3)*d/dx P(n-2,x) + (2*n^4-4*n^2+2+(4*n^4-8*n^2+4)*x)*P(n-1,x) - (4*n^4-8*n^2+4)*x^2*d/dx P(n-1,x) for n >= 2, with P(0,x) = 1, P(1,x) = 4 + 16*x.","mathematica":"P[0, x_] := 1;\nP[1, x_] := 4 + 16*x;\nP[n_, x_] := P[n, x] = Expand[Together[(-(n^4 + 2*n^3 + n^2 + (4*n^4 + 8*n^3 + 4*n^2)*x - (9*n^4 + 18*n^3 + 9*n^2)*x^2)*P[n - 2, x] + ((4*n^4 + 8*n^3 + 4*n^2)*x^2 + (4*n^4 + 8*n^3 + 4*n^2)*x^3)*D[P[n - 2, x], x] + (2*n^4 - 4*n^2 + 2 + (4*n^4 - 8*n^2 + 4)*x)*P[n - 1, x] - (4*n^4 - 8*n^2 + 4)*x^2*D[P[n - 1, x], x])/(n^4 - 2*n^3 + n^2)]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; v[2] = 4 + 16*x; for(n = 2, N, my(i = n + 1); v[i] = (-(n^4 + 2*n^3 + n^2 + (4*n^4 + 8*n^3 + 4*n^2)*x - (9*n^4 + 18*n^3 + 9*n^2)*x^2)*v[i - 2] + ((4*n^4 + 8*n^3 + 4*n^2)*x^2 + (4*n^4 + 8*n^3 + 4*n^2)*x^3)*deriv(v[i - 2], x) + (2*n^4 - 4*n^2 + 2 + (4*n^4 - 8*n^2 + 4)*x)*v[i - 1] - (4*n^4 - 8*n^2 + 4)*x^2*deriv(v[i - 1], x))/(n^4 - 2*n^3 + n^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-c8c19eba9d68881f","steps":["\u00d7(1+2n+n\u00b2)","(\u03b8+1)\u00b2"],"edges":["e-b78deffc64bc1942","e-b639f023f58d36b2"],"text":"A007318 \u2192 \u00d7(1+2n+n\u00b2) \u2192 (\u03b8+1)\u00b2"},"headline":"A007318 \u2192 \u00d7(1+2n+n\u00b2) \u2192 (\u03b8+1)\u00b2","chain":null}