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.

1, 3, 315, 155925, 212837625, 618718975875, 3287253918823875, 28845653137679503125, 388983632561608099640625, 7637693625347175036443671875, 209402646126143497974176151796875, 7752714167528210725497923667975703125, 377130780679409810741846496828678078515625

Offset

0,2

Comments

From Karol A. Penson, Oct 05 2009: (Start)

Integral representation as n-th moment of a positive function on a positive semi-axis (solution of the Stieltjes moment problem), in Maple notation:

a(n)=int(x^n*((1/4)*sqrt(2)*(Pi^(3/2)*2^(1/4)*hypergeom([], [1/2, 3/4], -(1/32)*x)*sqrt(x)-2*Pi*hypergeom([], [3/4, 5/4], -(1/32)*x)*GAMMA(3/4)*x^(3/4)+sqrt(Pi)*GAMMA(3/4)^2*2^(1/4)*hypergeom([], [5/4, 3/2],-(1/32)*x)*x)/(Pi^(3/2)*GAMMA(3/4)*x^(5/4))), x=0..infinity), n=0,1... .

This solution may not be unique. (End)

References

G. Pólya and G. Szegő, Problems and Theorems in Analysis II (Springer 1924, reprinted 1976), Appendix: Problem 203.1, p164.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..100

Eric Weisstein's World of Mathematics, Tournament

Index entries for sequences related to tornaments.

Formula

a(n) = (4*n)!/(n!*8^n).

a(n) = A001147(n)*A001147(2*n).

a(n) = A008977(n)*(A049606(n)/A001316(n))^3. - Reinhard Zumkeller, Apr 28 2008

Prog

(PARI) a(n)={(4*n)!/(n!*8^n)} \\ Andrew Howroyd, Jan 07 2020

Crossrefs

Cf. A008299, A000142, A100733, A001018.

Sequence in context: A134215 A361032 A034994 * A168440 A067667 A080976

Adjacent sequences: A139538 A139539 A139540 * A139542 A139543 A139544

Keyword

nonn

Author

Reinhard Zumkeller, Apr 25 2008

Extensions

Terms a(11) and beyond from Andrew Howroyd, Jan 07 2020

Status

approved