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100;\n  5: 180,  720,  1080,   720,   180;\n  6: 294, 1470,  2940,  2940,  1470,   294;\n  7: 448, 2688,  6720,  8960,  6720,  2688,   448;\n  8: 648, 4536, 13608, 22680, 22680, 13608,  4536,  648;\n  9: 900, 7200, 25200, 50400, 63000, 50400, 25200, 7200, 900;\n","recurrence_sentence":"The row polynomials satisfy (n^4-2*n^3+n^2)*P(n,x) = -(n^4+2*n^3+n^2+(2*n^4+4*n^3+2*n^2)*x+(n^4+2*n^3+n^2)*x^2)*P(n-2,x) + (2*n^4-4*n^2+2+(2*n^4-4*n^2+2)*x)*P(n-1,x) for n >= 2, with P(0,x) = 0, P(1,x) = 4.","mathematica":"P[0, x_] := 0;\nP[1, x_] := 4;\nP[n_, x_] := P[n, x] = Expand[Together[(-(n^4 + 2*n^3 + n^2 + (2*n^4 + 4*n^3 + 2*n^2)*x + (n^4 + 2*n^3 + n^2)*x^2)*P[n - 2, x] + (2*n^4 - 4*n^2 + 2 + (2*n^4 - 4*n^2 + 2)*x)*P[n - 1, 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] = 0; v[2] = 4; for(n = 2, N, my(i = n + 1); v[i] = (-(n^4 + 2*n^3 + n^2 + (2*n^4 + 4*n^3 + 2*n^2)*x + (n^4 + 2*n^3 + n^2)*x^2)*v[i - 2] + (2*n^4 - 4*n^2 + 2 + (2*n^4 - 4*n^2 + 2)*x)*v[i - 1])/(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)","D"],"edges":["e-b78deffc64bc1942","e-7f6c7a1231c5d5aa"],"text":"A007318 \u2192 \u00d7(1+2n+n\u00b2) \u2192 D"},"headline":"A007318 \u2192 \u00d7(1+2n+n\u00b2) \u2192 D","chain":null}