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 A249014 #14 Oct 21 2014 04:09:55
%S A249014 1,3,15,105,933,9951,123123,1727685,27050985,466795323,8791179831,
%T A249014 179262508833,3931730998605,92237649141015,2303515063987803,
%U A249014 60987344488950141,1705641174191204433,50228924171214633075,1553143164997199612895
%N A249014 A double binomial sum.
%F A249014 E.g.f.: (1/(1-t)^2)*exp((3*t-3*t^2+t^3)/(3*(1-t)^3)).
%F A249014 a(n) = sum(n!/k!*sum(bin(k,i)*bin(n+k-i+1,2*k+i+1)/3^i,i=0..k),k=0..n).
%F A249014 a(n) = sum(Lah(n,k)*h(k),k=0..n), where Lah(n,k) are the Lah numbers and the numbers h(n) are defined by the e.g.f. h(x) = (1+t)^2*exp(t+t^2+t^3/3) (essentially sequence A049425).
%F A249014 a(n) = sum(Lah(n+1,k+1)*h(k),k=0..n), where Lah(n,k) are the Lah numbers and the numbers h(n) are defined by the e.g.f. h(x) = exp(t+t^2+t^3/3) (sequence A049425).
%F A249014 a(n) = sum(bin(n,k)*(n!/k!)*h(k),k=0..n), where the numbers h(n) are defined by the e.g.f. h(x) = (1+t)*exp(t+t^2+t^3/3).
%F A249014 Recurrence: a(n+4)-(4*n+15)*a(n+3)+6*(n+3)^2*a(n+2)-2*(n+3)*(n+2)*(2n+5)*a(n+1)+(n+3)*(n+2)^2*(n+1)*a(n)=0.
%t A249014 Table[Sum[n!/k!Sum[Binomial[k,i]Binomial[n+k-i+1,2k+i+1]/3^i,{i,0,k}],{k,0,n}],{n,0,60}]
%o A249014 (Maxima) makelist(sum(n!/k!*sum(binomial(k,i)*binomial(n+k-i+1,2*k+i+1)/3^i,i,0,k),k,0,n),n,0,12);
%Y A249014 Cf. A049425.
%K A249014 nonn
%O A249014 0,2
%A A249014 _Emanuele Munarini_, Oct 20 2014