A292419 a(n) = [x^n] Product_{k>=1} (1 + n*x^k) / (1 - n*x^k).

1, 2, 12, 96, 872, 9960, 138180, 2298016, 44686224, 995739498, 24993249820, 697309946784, 21396151468536, 715827315312200, 25926440773118340, 1010478298772398080, 42162515927954808352, 1875027040759682964144, 88527520717734462201756, 4422273966757678408594560

Offset: 0

Author

Vaclav Kotesovec, Sep 16 2017

Keywords

• nonn

Comments

Convolution of A291698 and A124577.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..385

Crossrefs

Cf. A124577, A291698, A292418.

Programs

Mathematica

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

PARI

{a(n)= polcoef(prod(k=1, n, ((1+n*x^k)/(1-n*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^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.