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A320350

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

1, 1, 3, 20, 148, 1384, 15728, 207696, 3094152, 51423288, 945943512, 19083180192, 418550811600, 9907493349168, 251588827187280, 6820899616891008, 196645361557479552, 6007407711127690752, 193842462200078260224, 6586904673329133618432, 235079477736802622742528, 8790132360155070084076800

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A000009(k)*k!.

From Vaclav Kotesovec, Oct 13 2018: (Start)

a(n) ~ n! * exp(n + Pi*sqrt(n/(3*(exp(1) - 1))) + Pi^2/(24*(exp(1) - 1))) / (4 * 3^(1/4) * n^(3/4) * (exp(1) - 1)^(n + 1/4)).

a(n) ~ sqrt(Pi) * exp(Pi*sqrt(n/(3*(exp(1) - 1))) + Pi^2/(24*(exp(1) - 1))) * n^(n - 1/4) / (2^(3/2) * 3^(1/4) * (exp(1) - 1)^(n + 1/4)).

(End)

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