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 A261833 #32 Oct 05 2015 17:03:04
%S A261833 1,16,406,14866,740026,48026266,3937533706,397912444666,
%T A261833 48589663862026,7053101481134266,1200393616793282506,
%U A261833 236747809664852265466,53564655768153719942026,13780851677757681289022266,4000515700684222714620799306,1301419578177153109817779142266,471541578407011294721978551670026
%N A261833 a(n) = sum(stirling2(n,k)*(k+1)!*(k+3)!,k=1..n)/48.
%C A261833 It appears that for all n>1 the last digit of a(n) is 6.
%F A261833 Representation as a sum of infinite series of special values of hypergeometric functions of type 2F0, in Maple notation:
%F A261833 a(n) = sum(k^n*(k+1)!*(k+3)!*hypergeom([k+2,k+4],[],-1)/k!, k=1..infinity)/48, n=1,2,... .
%F A261833 a(n) ~ exp(1/2) * (n+1)! * (n+3)! / 48. - _Vaclav Kotesovec_, Oct 05 2015
%p A261833 with(combinat): a:= n-> sum(stirling2(n, k)*(k+1)!*(k+3)!, k=1..n)/48: seq(a(n), n=1..20);
%t A261833 Table[Sum[StirlingS2[n, k]*(k+1)!*(k+3)!, {k, 1, n}]/48, {n, 1, 20}] (* _Vaclav Kotesovec_, Oct 05 2015 *)
%K A261833 nonn
%O A261833 1,2
%A A261833 _Karol A. Penson_ and Katarzyna Gorska, Oct 02 2015