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 A109263 #12 May 26 2013 10:39:49
%S A109263 0,0,1,3,10,34,118,416,1485,5355,19473,71313,262735,973027,3619955,
%T A109263 13521307,50684778,190597594,718788034,2717755820,10300186824,
%U A109263 39121645886,148884623768,567643844338,2167882951110,8292331115104
%N A109263 A Catalan transform of F(n-1)-0^n.
%C A109263 A column of A109267.
%C A109263 Define a triangle by T(n,0)=A000045(n) and T(n,k)=sum_{r=k-1..n} T(r,k-1). (The column k=1 is A000071, the column k=2 is A001924 etc). Then T(n,n)=a(n+1). - _J. M. Bergot_, May 22 2013
%F A109263 G.f.: x^2c(x)^2/(1-xc(x)-x^2c(x)^2) where c(x) is the g.f. of A000108; a(n)=sum{k=0..n, (k/(2n-k))binomial(2n-k, n-k)(F(k-1)-0^k)}.
%F A109263 Conjecture: n*(n-3)*a(n) +2*(-4*n^2+15*n-10)*a(n-1) +(15*n^2-69*n+80)*a(n-2) +2*(n-2)*(2*n-5)*a(n-3)=0. - _R. J. Mathar_, Nov 09 2012
%K A109263 easy,nonn
%O A109263 0,4
%A A109263 _Paul Barry_, Jun 24 2005