%I A026585
%S A026585 1,0,2,2,8,14,40,86,222,518,1296,3130,7770,19066,47324,117094,
%T A026585 291260,724302,1806220,4507230,11266718,28188070,70609316,177023466,
%U A026585 444231564,1115639586,2803975860,7052132546,17748069294,44693162266
%N A026585 a(n)=T(n,n), T given by A026584. Also a(n) = number of integer strings 
               s(0),...,s(n) counted by T, such that s(n)=0.
%C A026585 The signed sequence 1,0,2,-2,8,-14,... is the inverse binomial transform 
               of A026569. - Paul Barry (pbarry(AT)wit.ie), Sep 09 2004
%H A026585 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 A026585 G.f.: sqrt[(1-x)/(1-x-4x^2)]. - Ralf Stephan, Jan 08 2004
%F A026585 Contribution from Paul Barry (pbarry(AT)wit.ie), Jul 01 2009: (Start)
%F A026585 G.f.: 1/(1-2x^2/(1-x-x^2/(1-x^2/(1-x-x^2/(1-x^2/(1-x-x^2/(1-... (continued 
               fraction);
%F A026585 a(0)=1, a(n)=sum{k=0..floor(n/2), (k/(n-k))C(n-k,k)*A000984(k)}. (End)
%Y A026585 Sequence in context: A045686 A045677 A005633 this_sequence A098273 A052970 
               A109190
%Y A026585 Adjacent sequences: A026582 A026583 A026584 this_sequence A026586 A026587 
               A026588
%K A026585 nonn
%O A026585 0,3
%A A026585 Clark Kimberling (ck6(AT)evansville.edu)