A362838 - OEIS

%I #11 May 05 2023 12:23:39

%S 1,0,4,27,704,26250,1573344,137145120,16494166016,2622125642472,

%T 532936224000000,134858889573071400,41584752648545107968,

%U 15351240982641183631440,6684412762278362097401856,3390180844777789569609375000,1981175610959755697378851553280

%N a(n) = (-1)^n * n! * Sum_{k=0..floor(n/2)} n^(n-k) * Stirling1(n-k,k)/(n-k)!.

%F a(n) = n! * [x^n] 1/(1 - n * x)^x.

%o (PARI) a(n) = (-1)^n*n!*sum(k=0, n\2, n^(n-k)*stirling(n-k, k, 1)/(n-k)!);

%Y Main diagonal of A362837.

%K nonn

%O 0,3

%A _Seiichi Manyama_, May 05 2023