%I #9 Nov 27 2017 07:35:57
%S 1,3,16,145,1926,33649,726328,18636561,553680370,18684924841,
%T 705833193924,29502690532393,1351724235304366,67359683340291105,
%U 3627011494019437936,209846445862386234529,12982402818188717219658
%N a(n) = (1/n!)*Sum_{k=0..n} (n+k)!.
%F a(n) ~ 2^(2*n + 1/2) * n^n / exp(n). - _Vaclav Kotesovec_, Nov 27 2017
%t Table[Sum[Binomial[n+k,k]k!,{k,0,n}],{n,0,100}] (* _Emanuele Munarini_, Sep 20 2016 *)
%o (Maxima) makelist(sum(binomial(n+k,k)*k!,k,0,n),n,0,12); // _Emanuele Munarini_, Sep 20 2016 //
%Y Cf. A111686.
%K easy,nonn
%O 0,2
%A _Vladeta Jovovic_, Aug 26 2005