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 A130522 #2 Mar 30 2012 18:37:04
%S A130522 1,1,3,8,25,89,349,1496,6962,34861,186678,1063591,6418167,40860485,
%T A130522 273513831,1919284246,14080876273,107750778177,858195666410,
%U A130522 7100543662976,60922480229704,541193416875432,4970306167860426
%N A130522 Diagonal immediately below the main diagonal of triangle A130521.
%C A130522 G.f. of column 0 (A127782) satisfies: G(x) = 1 + x*G(x+x^2); main diagonal of triangle A130521 equals column 0 shift left one place.
%F A130522 a(n) = Sum_{k=0..[n/2]+1} [C(n-k,k) + C(n-k+1,k-1)]*a(n-k-1) for n>=2, with a(0)=a(1)=1.
%o A130522 (PARI) {a(n)=if(n<0,0,if(n<=1,1,sum(k=0,n\2+1,(binomial(n-k,k)+binomial(n-k+1,k-1))*a(n-k-1))))}
%Y A130522 Cf. A130521 (triangle), A127782 (column 0).
%K A130522 nonn
%O A130522 0,3
%A A130522 _Paul D. Hanna_, Jun 02 2007