A292417 a(n) = [x^n] Product_{k>=1} 1/(1 - n^2*x^k).

1, 1, 20, 819, 70160, 10188775, 2240751636, 692647082799, 286013768613952, 151994274055319070, 101020305070908050100, 82086758986568812837856, 80056656965795630400382608, 92282612223268812357487227077, 124113156850218393012451734737460

Offset: 0

Author

Vaclav Kotesovec, Sep 16 2017

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..214

Crossrefs

Cf. A077335, A124577, A292304.

Programs

Mathematica

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

PARI

{a(n)= polcoef(prod(k=1, n, 1/(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) ~ n^(2*n) * (1 + 1/n^2 + 2/n^4 + 3/n^6 + 5/n^8 + 7/n^10), for coefficients see A000041.