A292416 a(n) = [x^n] Product_{k>=1} (1 + 2^n*x^k) / (1 - 2^n*x^k).

1, 4, 40, 1296, 149024, 71573568, 141871849600, 1143771307901184, 37183988027710374400, 4854666820584582571623424, 2540262650941956832151944038400, 5322109355556594174041950822678401024, 44623279107562668799968801377926722975965184

Offset: 0

Author

Vaclav Kotesovec, Sep 16 2017

Keywords

• nonn

Comments

Convolution of A292414 and A292415.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..57

Crossrefs

Cf. A292414, A292415.

Programs

Mathematica

nmax = 15; Table[SeriesCoefficient[Product[(1+2^n*x^k)/(1-2^n*x^k), {k, 1, n}], {x, 0, n}], {n, 0, nmax}]

PARI

{a(n)= polcoef(prod(k=1, n, ((1+2^n*x^k)/(1-2^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^2 + 1).