1,1

Special values of a sum of three hypergeometric functions of type 3F5.

In Maple notation:

a(n)=exp(-1)*3^(3*n)*((1/6)*(n!)^3*hypergeom([n+1, n+1, n+1],

[1, 1, 4/3, 5/3, 2], 1/27)+(3/8)*sqrt(3)*GAMMA(2/3)^3*GAMMA(n+1/3)^3*hypergeom([n+1/3, n+1/3, n+1/3]

, [1/3, 1/3, 1/3, 2/3, 4/3], 1/27)/Pi^3

+(1/2)*GAMMA(n+2/3)^3*hypergeom([n+2/3, n+2/3, n+2/3], [2/3, 2/3, 2/3, 4/3, 5/3], 1/27)/GAMMA(2/3)^3),

, n=1,2... .

Sequence in context: A004805 A123266 A034864 this_sequence A069642 A066162 A096725

Adjacent sequences: A157639 A157640 A157641 this_sequence A157643 A157644 A157645

nonn

Karol A. Penson (penson(AT)lptl.jussieu.fr), Mar 03 2009