A292418 a(n) = [x^n] Product_{k>=1} (1 + n^2*x^k) / (1 - n^2*x^k).
1, 2, 40, 1800, 149024, 21223800, 4609532520, 1414165715200, 581109518753920, 307788983933760954, 204081628466048180200, 165541724073121026987224, 161233041454793035411134240, 185663865439487951708529417080, 249499302292252719726304186789160
Offset: 0
Keywords
Links
- G. C. Greubel, Table of n, a(n) for n = 0..214
Programs
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Mathematica
nmax = 20; Table[SeriesCoefficient[Product[(1+n^2*x^k)/(1-n^2*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}] -
PARI
{a(n)= polcoef(prod(k=1, n, ((1+n^2*x^k)/(1-n^2*x^k) +x*O(x^n))), n)}; for(n=0,20, print1(a(n), ", ")) \\ G. C. Greubel, Feb 02 2019
Formula
a(n) ~ 2 * n^(2*n) * (1 + 2/n^2 + 4/n^4 + 8/n^6 + 14/n^8 + 24/n^10), for coefficients see A015128.
Comments