OFFSET
3,2
LINKS
Seiichi Manyama, Table of n, a(n) for n = 3..418
FORMULA
a(n) = Sum_{k=3..n} |Stirling1(n, k) * Stirling1(k, 3)|.
a(n) ~ (n-1)! * log(n)^2 / (2 * (1 - exp(-1))^n) * (1 + (2*gamma - 2*log(exp(1) - 1)) / log(n) + (gamma^2 - Pi^2/6 - 2*log(exp(1) - 1)*gamma + log(exp(1)-1)^2) / log(n)^2). - Vaclav Kotesovec, Jun 04 2022
MATHEMATICA
nmax = 22; CoefficientList[Series[-Log[1 + Log[1 - x]]^3/6, {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 3] &
Table[Sum[Abs[StirlingS1[n, k] StirlingS1[k, 3]], {k, 3, n}], {n, 3, 22}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 15 2021
STATUS
approved