OFFSET
0,3
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..250
Vaclav Kotesovec, Graph - the asymptotic ratio
FORMULA
Sum_{n>=0} a(n) * x^n / n!^2 = Sum_{n>=1} H(n) * (-log(1-x))^n / n!.
a(n) ~ n!^2 * (log(log(n)) + gamma + 1/log(n)), where gamma is the Euler-Mascheroni constant A001620. - Vaclav Kotesovec, Jun 03 2022
MATHEMATICA
Table[n! Sum[(-1)^(n - k) StirlingS1[n, k] HarmonicNumber[k], {k, 1, n}], {n, 0, 17}]
nmax = 17; CoefficientList[Series[Sum[HarmonicNumber[k] (-Log[1 - x])^k/k!, {k, 1, nmax}], {x, 0, nmax}], x] Range[0, nmax]!^2
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jun 03 2022
STATUS
approved