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 A110167 #14 Sep 04 2024 08:47:24
%S A110167 1,3,12,51,226,1026,4733,22083,103914,492228,2344035,11211210,
%T A110167 53817063,259135299,1251074772,6053946531,29354128498,142584834924,
%U A110167 693691007267,3379680991356,16486985580693,80521218046569,393674826425462
%N A110167 Diagonal sums of Riordan array A110165.
%H A110167 Vincenzo Librandi, <a href="/A110167/b110167.txt">Table of n, a(n) for n = 0..200</a>
%F A110167 G.f.: 2/sqrt(1-6*x+5*x^2)/(1+3*x+sqrt(1-6*x+5*x^2)).
%F A110167 a(n) = sum{k=0..floor(n/2), sum{j=0..n-k, C(n-k, j)*C(2*j, j+k)}}.
%F A110167 Recurrence: 3*(n+1)*(16*n-7)*a(n) = (272*n^2 + 9*n - 119)*a(n-1) - 3*(48*n^2 - 37*n - 31)*a(n-2) - 5*(n-1)*(16*n+9)*a(n-3). - _Vaclav Kotesovec_, Oct 18 2012
%F A110167 a(n) ~ 5^(n+3/2)/(8*sqrt(Pi*n)). - _Vaclav Kotesovec_, Oct 18 2012
%t A110167 Table[Sum[Sum[Binomial[n-k,j]*Binomial[2j,j+k],{j,0,n-k}],{k,0,Floor[n/2]}],{n,0,20}] (* _Vaclav Kotesovec_, Oct 18 2012 *)
%K A110167 easy,nonn
%O A110167 0,2
%A A110167 _Paul Barry_, Jul 14 2005