OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..413
FORMULA
E.g.f.: exp(Sum_{k>=1} sigma(k)*log(1/(1 - x))^k/k).
a(n) = Sum_{k=0..n} |Stirling1(n,k)|*A000041(k)*k!.
From Vaclav Kotesovec, Oct 13 2018: (Start)
a(n) ~ n! * exp(n + Pi*sqrt(2*n/(3*(exp(1) - 1))) + Pi^2/(12*(exp(1) - 1))) / (4 * sqrt(3) * n * (exp(1) - 1)^n).
a(n) ~ sqrt(Pi) * exp(Pi*sqrt(2*n/(3*(exp(1) - 1))) + Pi^2/(12*(exp(1) - 1))) * n^(n - 1/2) / (2^(3/2) * sqrt(3) * (exp(1) - 1)^n).
(End)
MAPLE
seq(n!*coeff(series(mul(1/(1-log(1/(1-x))^k), k=1..100), x=0, 21), x, n), n=0..20); # Paolo P. Lava, Jan 09 2019
MATHEMATICA
nmax = 20; CoefficientList[Series[Product[1/(1 - Log[1/(1 - x)]^k), {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!
nmax = 20; CoefficientList[Series[Exp[Sum[DivisorSigma[1, k] Log[1/(1 - x)]^k/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Abs[StirlingS1[n, k]] PartitionsP[k] k!, {k, 0, n}], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Oct 11 2018
STATUS
approved