A330499 Expansion of e.g.f. Sum_{k>=1} log(1 + log(1/(1 - x))^k).

0, 1, 2, 13, 71, 558, 5344, 60926, 766898, 10759096, 168848256, 2947203048, 56368708824, 1165246323408, 25802649445728, 609940593443952, 15377212949988624, 412827548455415040, 11764577341464710016, 354392697960438122880, 11237993013428254071936

Offset: 0

Author

Vaclav Kotesovec, Dec 16 2019

Keywords

• nonn

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 0..400
• Vaclav Kotesovec, Graph - the asymptotic ratio

Crossrefs

Cf. A007840, A330354, A330388, A330494, A330498.

Programs

Mathematica

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

Formula

a(n) ~ n! * c / (1 - exp(-1))^n, where c = 0.478656...