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 A367011 #15 Dec 31 2023 10:22:36
%S A367011 1,1,3,11,51,287,1899,14447,124251,1192127,12623979,146250287,
%T A367011 1840024251,24983863967,364140992139,5670546353807,93960923507931,
%U A367011 1650688221777407,30646388716777899,599565840087487727,12328458398407260411
%N A367011 a(n) = Sum_{k=0..n} k! * k^(n-k).
%H A367011 Seiichi Manyama, <a href="/A367011/b367011.txt">Table of n, a(n) for n = 0..449</a>
%F A367011 a(n) ~ Pi * n^(n+1) / exp(n).
%F A367011 a(n) ~ sqrt(Pi*n/2) * n!.
%t A367011 Table[Sum[k! * k^(n-k), {k, 0, n}], {n, 1, 20}]
%o A367011 (PARI) a(n) = sum(k=0, n, k!*k^(n-k)); \\ _Seiichi Manyama_, Dec 31 2023
%Y A367011 Cf. A026898, A112541, A367012.
%Y A367011 Cf. A003422, A233449, A368555.
%K A367011 nonn
%O A367011 0,3
%A A367011 _Vaclav Kotesovec_, Nov 01 2023
%E A367011 a(0)=1 prepended by _Seiichi Manyama_, Dec 31 2023