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

0,2

Comments

Convolution of A305127 and A318769.

Links

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

Formula

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

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]!

Crossrefs

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

Sequence in context: A223127 A361407 A323666 * A371547 A130721 A167449

Adjacent sequences: A318811 A318812 A318813 * A318815 A318816 A318817

Keyword

nonn

Author

Vaclav Kotesovec, Sep 04 2018

Status

approved