Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #5 Jun 06 2019 21:59:48
%S 1,1,27,104149,192052025697,401307330353526478576,
%T 1891640643805444860923624673784723,
%U 35720630453521390599442254755998585843785410691847,4425335738067265257031641848982502946902371654704454173556393591653249
%N a(n) = exp(-1) * Sum_{k>=0} (k + n - 1)!^n/(k!*(k - 1)!^n).
%F a(n) = A182933(n,n).
%t Table[Exp[-1] Sum[(k + n - 1)!^n/(k! (k - 1)!^n), {k, 0, Infinity}], {n, 0, 8}]
%Y Main diagonal of A182933.
%Y Cf. A000110, A070227, A094577.
%K nonn
%O 0,3
%A _Ilya Gutkovskiy_, Jun 06 2019