This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A109398 #13 Dec 31 2024 13:44:35
%S A109398 1,3,16,145,1926,33649,726328,18636561,553680370,18684924841,
%T A109398 705833193924,29502690532393,1351724235304366,67359683340291105,
%U A109398 3627011494019437936,209846445862386234529,12982402818188717219658
%N A109398 a(n) = (1/n!)*Sum_{k=0..n} (n+k)!.
%F A109398 a(n) ~ 2^(2*n + 1/2) * n^n / exp(n). - _Vaclav Kotesovec_, Nov 27 2017
%t A109398 Table[Sum[Binomial[n+k,k]k!,{k,0,n}],{n,0,100}] (* _Emanuele Munarini_, Sep 20 2016 *)
%o A109398 (Maxima) makelist(sum(binomial(n+k,k)*k!,k,0,n),n,0,12); /* _Emanuele Munarini_, Sep 20 2016 */
%Y A109398 Cf. A111686.
%K A109398 easy,nonn
%O A109398 0,2
%A A109398 _Vladeta Jovovic_, Aug 26 2005