OFFSET
1,1
COMMENTS
Special values of a sum of three hypergeometric functions of type 3F5.
In Maple notation:
FORMULA
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... .
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Mar 03 2009
STATUS
approved