A139541 - OEIS

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

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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