OFFSET
5,2
FORMULA
a(n) = Stirling2(n,5) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,5) * k * a(k).
a(n) ~ (n-1)! / (log(120^(1/5) + 1))^n. - Vaclav Kotesovec, Aug 09 2021
MATHEMATICA
nmax = 24; CoefficientList[Series[-Log[1 - (Exp[x] - 1)^5/5!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 5] &
a[n_] := a[n] = StirlingS2[n, 5] + (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 5] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 5, 24}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 08 2021
STATUS
approved