%I A024492
%S A024492 1,5,42,429,4862,58786,742900,9694845,129644790,1767263190,24466267020,
%T A024492 343059613650,4861946401452,69533550916004,1002242216651368,
%U A024492 14544636039226909,212336130412243110,3116285494907301262
%N A024492 Catalan numbers with odd index: a(n) = binomial(4*n+2,2*n+1)/(2*n+2).
%C A024492 Cf. A048990 (Catalan numbers with even index), A024491, A000108.
%F A024492 G.f.: A(x) = 1/2*x^-1*(1-sqrt(1/2*(1+sqrt(1-16*x)))).
%F A024492 a(n)=4^n*binomial(2n+1/2, n)/(n+1); - Paul Barry (pbarry(AT)wit.ie), 
               May 10 2005
%F A024492 a(n)=C(4n+1,2n+1)/(n+1); - Paul Barry (pbarry(AT)wit.ie), Nov 09 2006
%e A024492 sqrt(1/2*(1+sqrt(1-x))) = 1 - 1/8*x - 5/128*x^2 - 21/1024*x^3 - ...
%p A024492 with(combstruct):bin := {B=Union(Z,Prod(B,B))}: seq (count([B,bin,unlabeled],
               size=2*n), n=1..18); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Dec 05 2007
%o A024492 (Mupad) combinat::catalan(2*n+1)$ n = 0..24 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Jul 02 2008
%o A024492 (Mupad) combinat::dyckWords::count(2*n+1)$ n = 0..24 - Zerinvary Lajos 
               (zerinvarylajos(AT)yahoo.com), Jul 02 2008
%Y A024492 Sequence in context: A062021 A082145 A126765 this_sequence A005789 A151334 
               A102693
%Y A024492 Adjacent sequences: A024489 A024490 A024491 this_sequence A024493 A024494 
               A024495
%K A024492 nonn,easy,nice
%O A024492 0,2
%A A024492 Clark Kimberling (ck6(AT)evansville.edu)
%E A024492 More terms from Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)