A330445 Expansion of e.g.f.: Sum_{k>=1} log(1 + (exp(x) - 1)^k)/k.

0, 1, 1, 5, 19, 89, 691, 7265, 74299, 722489, 8224291, 130439825, 2456898379, 45287950889, 781106871091, 13479917085185, 268959501687259, 6688186010251289, 187628967639969091, 5285049770439071345, 144061583071243096939

Offset: 0

Author

Vaclav Kotesovec, Dec 15 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A330351.

Programs

Mathematica

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

Formula

E.g.f.: log(Product_{k>=1} (1 + (exp(x) - 1)^k)^(1/k)).

Conjecture: a(n) ~ (n-1)! / (log(2))^(n-1).