Search: id:A001448
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%I A001448
%S A001448 1,6,70,924,12870,184756,2704156,40116600,601080390,9075135300,
%T A001448 137846528820,2104098963720,32247603683100,495918532948104,
%U A001448 7648690600760440,118264581564861424,1832624140942590534
%N A001448 C(4n,2n) = (4*n)!/((2*n)!*(2*n)!).
%H A001448 T. D. Noe, <a href="b001448.txt">Table of n, a(n) for n=0..100</a>
%F A001448 Using Stirling's formula in sequence A000142 it is easy to get the asymptotic 
               expression a(n) ~ 16^n / sqrt(2 * Pi * n) - Dan Fux (dan.fux(AT)OpenGaia.com 
               or danfux(AT)OpenGaia.com), Apr 07 2001
%F A001448 a(n)= 2*A001700(2*n-1) = (2*n+1)*C(2*n), n >= 1, C(n) := A000108(n) (Catalan). 
               G.f.: (1-y*((1+4*y)*c(y)-(1-4*y)*c(-y)))/(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 A001448 a(n) ~ 2^(-1/2)*pi^(-1/2)*n^(-1/2)*2^(4*n)*{1 - 1/16*n^-1 + ...} - Joe 
               Keane (jgk(AT)jgk.org), Jun 11 2002
%p A001448 f := n->(4*n)!/((2*n)!*(2*n)!);
%p A001448 a:=n->sum(binomial(2*n,n)/(n+1), j=0..n): seq(a(n*2), n=0..16); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 30 2007
%Y A001448 Bisection of A000984. Cf. A002458.
%Y A001448 Sequence in context: A098639 A048708 A104900 this_sequence A024489 A036361 
               A050788
%Y A001448 Adjacent sequences: A001445 A001446 A001447 this_sequence A001449 A001450 
               A001451
%K A001448 nonn,nice,easy
%O A001448 0,2
%A A001448 N. J. A. Sloane (njas(AT)research.att.com).

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