Search: id:A002897
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%I A002897 M4580 N1952
%S A002897 1,8,216,8000,343000,16003008,788889024,40424237568,2131746903000,
%T A002897 114933031928000,6306605327953216,351047164190381568,
%U A002897 19774031697705428416,1125058699232216000000,64561313052442296000000
%N A002897 C(2n,n)^3.
%D A002897 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002897 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 
               (includes this sequence).
%D A002897 David H. Bailey, Jonathan M. Borwein, David Broadhurst and M. L. Glasser, 
               Elliptic integral evaluations of Bessel moments, arXiv:0801.0891.
%D A002897 C. Domb, On the theory of cooperative phenomena in crystals, Advances 
               in Phys., 9 (1960), 149-361.
%D A002897 S. Ramanujan, Modular Equations and Approximations to pi, pp. 23-39 of 
               Collected Papers of Srinivasa Ramanujan, Ed. G. H. Hardy et al., 
               AMS Chelsea 2000. See page 36, equation (25).
%F A002897 Expansion of (K(k)/(pi/2))^2 in powers of (kk'/4)^2, where K(k) is complete 
               elliptic integral of first kind evaluated at modulus k. - Michael 
               Somos, Jan 31 2007
%F A002897 G.f.: F(1/2, 1/2, 1/2; 1, 1; 64x) where F() is a hypergeometric function. 
               - Michael Somos, Jan 31 2007
%t A002897 a[n_]:= Coefficient[ Series[ HypergeometricPFQ[ {1/2, 1/2, 1/2}, {1, 
               1}, 64x], {x, 0, n}], x, n]
%o A002897 (PARI) {a(n)= binomial(2*n, n)^3} /* Michael Somos 31 Jan 2007 */
%o A002897 (Other) sage: [binomial(2*n,n)**3 for n in xrange(0, 17)] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Apr 21 2009]
%Y A002897 Sequence in context: A069045 A123057 A009072 this_sequence A024289 A009106 
               A000442
%Y A002897 Adjacent sequences: A002894 A002895 A002896 this_sequence A002898 A002899 
               A002900
%K A002897 nonn
%O A002897 0,2
%A A002897 N. J. A. Sloane (njas(AT)research.att.com), Simon Plouffe (simon.plouffe(AT)gmail.com)

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