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 A249062 #7 Oct 21 2014 04:09:44
%S A249062 1,2,5,18,69,306,1497,7890,45033,273474,1760301,11961522,85265325,
%T A249062 636026418,4947725889,40019230386,335868650577,2918173355010,
%U A249062 26199114476373,242657102748114,2314964975130261,22717352863875762,229029972003647145,2369438933865972498
%N A249062 A double binomial sum.
%F A249062 a(n) = sum((n!/k!)*sum(bin(k,i)*bin(k-i+1,n-k-2*i)/3^i,i=0..k),k=0..n).
%F A249062 E.g.f.: (1+t)*exp(t+t^2+t^3/3).
%F A249062 a(n+4)+(n+1)*a(n+3)-3*(n+3)*a(n+2)-3*(n+3)*(n+2)*a(n+1)-(n+3)*(n+2)*(n+1)*a(n)=0.
%t A249062 AList[n_] := CoefficientList[Series[(1 + t) E^(t + t^2 + t^3/3), {t, 0, n}], t] Table[k!, {k, 0, n}]
%t A249062 AList[100]
%o A249062 (Maxima) a(n) := sum((n!/k!)*sum(binomial(k,i)*binomial(k-i+1,n-k-2*i)/3^i,i,0,k),k,0,n);
%o A249062 makelist(a(n),n,0,24);
%Y A249062 Cf. A049425.
%K A249062 nonn
%O A249062 0,2
%A A249062 _Emanuele Munarini_, Oct 20 2014