%I #6 May 21 2019 03:49:28
%S 1,0,3,50,1449,61724,3608515,275520972,26505128433,3125830471928,
%T 442286373458691,73789189395157730,14309059313820886681,
%U 3186711239965235356776,806772967716453793227523,230153293624841114893344854,73420355768107554901016231265
%N a(n) = n! * [x^n] exp(exp(n*x)/(1 + x) - 1).
%t Table[n! SeriesCoefficient[Exp[Exp[n x]/(1 + x) - 1], {x, 0, n}], {n, 0, 16}]
%Y Cf. A134095, A292914, A308330, A321989.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, May 20 2019