0,2

Contribution from Karol A. Penson (penson(AT)lptl.jussieu.fr), Oct 05 2009: (Start)

Integral representation as n-th moment of a positive function on a positive

halfaxis (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)

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

Eric Weisstein's World of Mathematics, Tournament

Index entries for sequences related to tornaments.

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

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

Cf. A008299, A000142, A100733, A001018.

Sequence in context: A039954 A134215 A034994 this_sequence A067667 A080976 A160070

Adjacent sequences: A139538 A139539 A139540 this_sequence A139542 A139543 A139544

nonn

Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 25 2008