A318814 Expansion of e.g.f. Product_{k>=1} ((1 + x^k)/(1 - x^k))^(sigma(k)/k).

1, 2, 10, 64, 512, 4768, 53056, 645440, 8868352, 133302016, 2184149504, 38530160128, 733246566400, 14834910150656, 319778313883648, 7292507623063552, 175517505539538944, 4440588163825008640, 117969026857318678528, 3276703253565946855424, 95086071773832697348096

Offset: 0

Author

Vaclav Kotesovec, Sep 04 2018

Keywords

• nonn

Comments

Convolution of A305127 and A318769.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..436

Crossrefs

Cf. A000203, A305127, A301554, A301555, A318769.

Programs

Mathematica

nmax = 20; CoefficientList[Series[Product[((1+x^k)/(1-x^k))^(DivisorSigma[1, k]/k), {k, 1, nmax}], {x, 0, nmax}], x] * Range[0, nmax]!

Formula

log(a(n)/n!) ~ Pi^2 * sqrt(n/6).