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 A070227 #23 May 01 2025 08:57:29
%S A070227 1,1,7,2971,326922081,25571928251231076,3104750712141723393459934903,
%T A070227 1106411839720559249283387766293758050197271,
%U A070227 1982711933502621451047063899803427489760228712955842831202561
%N A070227 a(n) = Sum_{k>=0} (k+n)!^n/((k+n)!*(k!^n)*exp(1)).
%H A070227 Amiram Eldar, <a href="/A070227/b070227.txt">Table of n, a(n) for n = 0..24</a>
%F A070227 a(n) = A090210(n,n). - _Alois P. Heinz_, Aug 01 2016
%F A070227 a(n) = Sum_{k=n..n^2} Sum_{m=n..k} (-1)^(k+m) * m!^(n-1) / ((k-m)! * (m-n)!^n). - _Vaclav Kotesovec_, May 01 2025
%t A070227 a[n_] := Exp[-1] * Sum[(k + n)!^n/((k + n)!*(k!^n)), {k, 0, Infinity}]; Array[a, 10, 0] (* _Amiram Eldar_, May 01 2025 *)
%t A070227 Table[Sum[(-1)^(k+m) * m!^(n-1) / ((k-m)!*(m-n)!^n), {k, n, n^2}, {m, n, k}], {n, 0, 10}] (* _Vaclav Kotesovec_, May 01 2025 *)
%o A070227 (PARI) \\ precision 1000 digits :
%o A070227 for(n=1,9,print1(round(sum(k=0,200,(k+n)!^n/((k+n)!*(k!^n)*exp(1)))),","))
%Y A070227 Cf. A090210.
%K A070227 easy,nonn
%O A070227 0,3
%A A070227 _Benoit Cloitre_, May 07 2002
%E A070227 a(0)=1 prepended by _Alois P. Heinz_, Aug 01 2016