%I A002458
%S A002458 1,10,126,1716,24310,352716,5200300,77558760,1166803110,17672631900,
%T A002458 269128937220,4116715363800,63205303218876,973469712824056,15033633249770520,
%U A002458 232714176627630544,3609714217008132870,56093138908331422716,873065282167813104916
%N A002458 C(4n+1,2n).
%D A002458 The right-hand side of a binomial coefficient identity in H. W. Gould, 
               Combinatorial Identities, Morgantown, 1982, (3.109), page 35.
%H A002458 T. D. Noe, <a href="b002458.txt">Table of n, a(n) for n=0..100</a>
%F A002458 a(n)= A001700(2*n) = (n+1)*C(2*n+1), C(n) := A000108(n) (Catalan).
%F A002458 G.f.: (4-(1+4*y)*c(y)-(1-4*y)*c(-y))/(2*(1-(4*y)^2)) with y^2=x, c(y)= 
               g.f. for A000108 (Catalan). - Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), 
               Dec 13 2001
%F A002458 a(n) ~ 2^(1/2)*pi^(-1/2)*n^(-1/2)*2^(4*n)*{1 - 5/16*n^-1 + ...} - Joe 
               Keane (jgk(AT)jgk.org), Jun 11 2002
%Y A002458 Cf. A000984, A001448.
%Y A002458 Sequence in context: A097816 A079609 A101599 this_sequence A079241 A007819 
               A054050
%Y A002458 Adjacent sequences: A002455 A002456 A002457 this_sequence A002459 A002460 
               A002461
%K A002458 nonn,easy,nice
%O A002458 0,2
%A A002458 N. J. A. Sloane (njas(AT)research.att.com).