OFFSET
0,3
FORMULA
From Vaclav Kotesovec, Oct 28 2024: (Start)
a(n) ~ (n!)^(n-1).
a(n) ~ (2*Pi)^((n-1)/2) * n^(n^2 - n/2 - 1/2) / exp(n^2 - n - 1/12). (End)
MATHEMATICA
Table[(n!)^n SeriesCoefficient[Exp[Sum[x^k/k^n, {k, 1, n}]], {x, 0, n}], {n, 0, 10}]
b[n_, k_] := If[n == 0, 1, (1/n) Sum[(Binomial[n, j] (n - j - 1)!)^k (n - j) b[j, k], {j, 0, n - 1}]]; a[n_] := b[n, n]; Table[a[n], {n, 0, 10}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jul 21 2020
STATUS
approved