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 A081124 #19 Feb 02 2017 15:25:40
%S A081124 1,2,4,8,17,38,90,224,585,1594,4520,13288,40409,126782,409646,1360512,
%T A081124 4637681,16202034,57941164,211860488,791272129,3015807254,11719800674,
%U A081124 46401584096,187039192185,767058993386,3198568491792,13553864902504
%N A081124 Binomial transform of floor(n/2)!.
%H A081124 G. C. Greubel, <a href="/A081124/b081124.txt">Table of n, a(n) for n = 0..880</a>
%H A081124 Adam M. Goyt and Lara K. Pudwell, <a href="http://arxiv.org/abs/1203.3786">Avoiding colored partitions of two elements in the pattern sense</a>, arXiv:1203.3786 [math.CO], 2012. - From _N. J. A. Sloane_, Sep 17 2012
%F A081124 a(n) = Sum_{k=0..n} C(n, k)*floor(k/2)!.
%F A081124 E.g.f.: exp(x)*(1+sqrt(Pi)/2*(x+2)*exp(x^2/4)*erf(x/2)). - _Vladeta Jovovic_, Sep 25 2003
%F A081124 Conjecture: 2*a(n) -4*a(n-1) +(-n+2)*a(n-2) +(n-1)*a(n-3)=0. - _R. J. Mathar_, Nov 24 2012
%F A081124 a(n) ~ sqrt(Pi*n)/2 * exp(sqrt(2*n)-n/2-1/2)*(n/2)^(n/2) * (1+5/(3*sqrt(2*n))). - _Vaclav Kotesovec_, Aug 15 2013
%t A081124 Table[Sum[Binomial[n,k]*Floor[k/2]!,{k,0,n}],{n,0,20}] (* _Vaclav Kotesovec_, Aug 15 2013 *)
%o A081124 (PARI) for(n=0,50, print1(sum(k=0,n, binomial(n,k)*(floor(k/2))!), ", ")) \\ _G. C. Greubel_, Feb 02 2017
%Y A081124 Cf. A081123, A004526.
%Y A081124 Cf. A084261.
%K A081124 easy,nonn
%O A081124 0,2
%A A081124 _Paul Barry_, Mar 07 2003