A362838 a(n) = (-1)^n * n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling1(n-k,k)/(n-k)!.
1, 0, 4, 27, 704, 26250, 1573344, 137145120, 16494166016, 2622125642472, 532936224000000, 134858889573071400, 41584752648545107968, 15351240982641183631440, 6684412762278362097401856, 3390180844777789569609375000, 1981175610959755697378851553280
Offset: 0
Crossrefs
Main diagonal of A362837.
Programs
-
Mathematica
Table[n!*SeriesCoefficient[1/(1 - n*x)^x, {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Aug 30 2025 *) -
PARI
a(n) = (-1)^n*n!*sum(k=0, n\2, n^(n-k)*stirling(n-k, k, 1)/(n-k)!);
Formula
a(n) = n! * [x^n] 1/(1 - n * x)^x.
a(n) ~ sqrt(2*Pi) * n^(2*n - 3/2) / exp(n). - Vaclav Kotesovec, Aug 30 2025