%I A139541
%S A139541 1,3,315,155925,212837625,618718975875,3287253918823875,
%T A139541 28845653137679503125,388983632561608099640625,
%U A139541 7637693625347175036443671875,209402646126143497974176151796875
%N A139541 There are 4*n players who wish to play bridge at n tables. Each player 
               must have another player as partner and each pair of partners must 
               have another pair as opponents. The choice of partners and opponents 
               can be made in exactly a(n)=(4*n)!/(n!*8^n) different ways.
%C A139541 Contribution from Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 05 
               2009: (Start)
%C A139541 Integral representation as n-th moment of a positive function on a positive
%C A139541 halfaxis (solution of the Stieltjes moment problem), in Maple notation:
%C A139541 a(n)=int(x^n*((1/4)*sqrt(2)*(Pi^(3/2)*2^(1/4)*hypergeom([], [1/2, 3/4],
%C A139541 -(1/32)*x)*sqrt(x)-2*Pi*hypergeom([], [3/4, 5/4], -(1/32)*x)*GAMMA(3/
               4)*x^(3/4)
%C A139541 +sqrt(Pi)*GAMMA(3/4)^2*2^(1/4)*hypergeom([], [5/4, 3/2],
%C A139541 -(1/32)*x)*x)/(Pi^(3/2)*GAMMA(3/4)*x^(5/4))), x=0..infinity), n=0,1... 
               .
%C A139541 This solution may not be unique. (End)
%D A139541 G. Polya and G. Szego, Problems and Theorems in Analysis II (Springer 
               1924, reprinted 1976), Appendix: Problem 203.1, p164.
%H A139541 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Tournament.html">Tournament</a>
%H A139541 <a href="Sindx_To.html#tournament">Index entries for sequences related 
               to tornaments</a>.
%F A139541 a(n) = A001147(n)*A001147(2*n).
%F A139541 a(n) = A008977(n)*(A049606(n)/A001316(n))^3. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Apr 28 2008
%Y A139541 Cf. A008299, A000142, A100733, A001018.
%Y A139541 Sequence in context: A039954 A134215 A034994 this_sequence A067667 A080976 
               A160070
%Y A139541 Adjacent sequences: A139538 A139539 A139540 this_sequence A139542 A139543 
               A139544
%K A139541 nonn
%O A139541 0,2
%A A139541 Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2008