OFFSET
3,2
FORMULA
a(n) = Stirling2(n,3) + (1/n) * Sum_{k=1..n-1} binomial(n,k) * Stirling2(n-k,3) * k * a(k).
a(n) ~ (n-1)! / (log(6^(1/3)+1))^n. - Vaclav Kotesovec, Aug 09 2021
MATHEMATICA
nmax = 23; CoefficientList[Series[-Log[1 - (Exp[x] - 1)^3/3!], {x, 0, nmax}], x] Range[0, nmax]! // Drop[#, 3] &
a[n_] := a[n] = StirlingS2[n, 3] + (1/n) Sum[Binomial[n, k] StirlingS2[n - k, 3] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 3, 23}]
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(-log(1-(exp(x)-1)^3/3!))) \\ Michel Marcus, Aug 09 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 08 2021
STATUS
approved