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 A186334 #10 Oct 30 2017 06:13:00
%S A186334 1,1,3,5,12,24,56,123,291,677,1637,3954,9757,24171,60648,152929,
%T A186334 388822,993216,2551808,6582899,17055507,44341141,115671498,302627130,
%U A186334 793951897,2088103609,5504504961,14541271283,38489869502,102066761622,271122837895
%N A186334 A transform of the Catalan numbers.
%C A186334 Hankel transform is A094967(n+1) (F(2n+1) repeated).
%F A186334 a(n)=sum{k=0..n, sum{j=0..n, binomial(k-j,n-k-j)*binomial(k,j)*if(n-k-j>=0, A000108(n-k-j),0)}}
%F A186334 Conjecture: (n+2)*a(n) +2*(-n-1)*a(n-1) +(-5*n+4)*a(n-2) +2*(3*n-4)*a(n-3) +5*(n-2)*a(n-4)=0. - _R. J. Mathar_, Nov 07 2014
%F A186334 a(n) ~ 21^(1/4) * ((1+sqrt(21))/2)^(n + 5/2) / (8 * sqrt(Pi) * n^(3/2)). - _Vaclav Kotesovec_, Oct 30 2017
%t A186334 Table[Sum[Sum[Binomial[k-j,n-k-j] * Binomial[k,j] * If[n-k-j>=0, CatalanNumber[n-k-j], 0], {j,0,n}], {k,0,n}], {n,0,30}] (* _Vaclav Kotesovec_, Oct 30 2017 *)
%Y A186334 Cf. A186335.
%K A186334 nonn,easy
%O A186334 0,3
%A A186334 _Paul Barry_, Feb 18 2011