%I A026569
%S A026569 1,1,3,5,13,27,67,153,375,893,2189,5319,13089,32155,79479,196573,
%T A026569 487833,1212135,3018355,7525585,18792303,46980373,117589689,294613155,
%U A026569 738844719,1854484305,4658460165,11710592711,29458662005,74151824271
%N A026569 a(n)=T(n,n), T given by A026568. Also a(n) = number of integer strings 
               s(0),...,s(n) counted by T, such that s(n)=0.
%H A026569 J. W. Layman, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               The Hankel Transform and Some of its Properties</a>, J. Integer Sequences, 
               4 (2001), #01.1.5.
%F A026569 a(n)=sum{k=0..floor(n/2), binomial(2k, k)binomial(n-k, k)} - Paul Barry 
               (pbarry(AT)wit.ie), Sep 09 2004
%F A026569 G.f.: sqrt[1/((1-x)(1-x-4x^2))]. - Ralf Stephan, Jan 08 2004
%F A026569 n*a(n)=(2*n-1)*a(n-1)+(3*n-3)*a(n-2)-(4*n-6)*a(n-3). - Vladeta Jovovic 
               (vladeta(AT)eunet.rs), Mar 12 2005
%F A026569 a(n)=sum{k=0..n, C(k, n-k)C(2(n-k), n-k)}; - Paul Barry (pbarry(AT)wit.ie), 
               Jul 30 2005
%F A026569 G.f.: 1/(1-x-2x^2/(1-0x-x^2/(1-x-x^2/(1-0x-2x^2/(1-x-x^2/.... (continued 
               fraction). [From Paul Barry (pbarry(AT)wit.ie), Dec 07 2008]
%Y A026569 Sequence in context: A141630 A084173 A000631 this_sequence A035082 A005198 
               A160823
%Y A026569 Adjacent sequences: A026566 A026567 A026568 this_sequence A026570 A026571 
               A026572
%K A026569 nonn
%O A026569 0,3
%A A026569 Clark Kimberling (ck6(AT)evansville.edu)