login
a(n) = [x^n] Product_{k>=1} (1 + n*x^k) / (1 - n*x^k).
3

%I #7 Feb 02 2019 04:32:48

%S 1,2,12,96,872,9960,138180,2298016,44686224,995739498,24993249820,

%T 697309946784,21396151468536,715827315312200,25926440773118340,

%U 1010478298772398080,42162515927954808352,1875027040759682964144,88527520717734462201756,4422273966757678408594560

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

%C Convolution of A291698 and A124577.

%H G. C. Greubel, <a href="/A292419/b292419.txt">Table of n, a(n) for n = 0..385</a>

%F a(n) ~ 2 * n^n * (1 + 2/n + 4/n^2 + 8/n^3 + 14/n^4 + 24/n^5 + 40/n^6 + 64/n^7 + 100/n^8 + 154/n^9 + 232/n^10), for coefficients see A015128.

%t nmax = 25; Table[SeriesCoefficient[Product[(1+n*x^k)/(1-n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

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

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

%Y Cf. A124577, A291698, A292418.

%K nonn

%O 0,2

%A _Vaclav Kotesovec_, Sep 16 2017