A292417 - OEIS

%I #9 Feb 02 2019 04:32:23

%S 1,1,20,819,70160,10188775,2240751636,692647082799,286013768613952,

%T 151994274055319070,101020305070908050100,82086758986568812837856,

%U 80056656965795630400382608,92282612223268812357487227077,124113156850218393012451734737460

%N a(n) = [x^n] Product_{k>=1} 1/(1 - n^2*x^k).

%H G. C. Greubel, <a href="/A292417/b292417.txt">Table of n, a(n) for n = 0..214</a>

%F a(n) ~ n^(2*n) * (1 + 1/n^2 + 2/n^4 + 3/n^6 + 5/n^8 + 7/n^10), for coefficients see A000041.

%t nmax = 20; Table[SeriesCoefficient[Product[1/(1-n^2*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

%o (PARI) {a(n)= polcoef(prod(k=1, n, 1/(1-n^2*x^k +x*O(x^n))), n)};

%o for(n=0,20, print1(a(n), ", ")) \\ _G. C. Greubel_, Feb 02 2019

%Y Cf. A077335, A124577, A292304.

%K nonn

%O 0,3

%A _Vaclav Kotesovec_, Sep 16 2017