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A330445 Expansion of e.g.f.: Sum_{k>=1} log(1 + (exp(x) - 1)^k)/k. 2
0, 1, 1, 5, 19, 89, 691, 7265, 74299, 722489, 8224291, 130439825, 2456898379, 45287950889, 781106871091, 13479917085185, 268959501687259, 6688186010251289, 187628967639969091, 5285049770439071345, 144061583071243096939 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

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

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

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]!

CROSSREFS

Cf. A330351.

Sequence in context: A110210 A244899 A147139 * A149805 A149806 A149807

Adjacent sequences:  A330442 A330443 A330444 * A330446 A330447 A330448

KEYWORD

nonn

AUTHOR

Vaclav Kotesovec, Dec 15 2019

STATUS

approved

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Last modified April 23 10:07 EDT 2021. Contains 343204 sequences. (Running on oeis4.)