OFFSET
1,1
COMMENTS
Special values of a sum of three hypergeometric functions of type 4F6.
In Maple notation:
FORMULA
a(n)=exp(-1)*3^(4*n)*((1/6)*(n!)^4*hypergeom([n+1, n+1, n+1, n+1],
[1, 1, 1, 4/3, 5/3, 2], 1/27)+(9/16)*GAMMA(2/3)^4*GAMMA(n+1/3)^4
*hypergeom([n+1/3, n+1/3, n+1/3, n+1/3], [1/3, 1/3, 1/3, 1/3, 2/3, 4/3],
1/27)/Pi^4+(1/2)*GAMMA(n+2/3)^4*hypergeom([n+2/3, n+2/3, n+2/3, n+2/3]
, [2/3, 2/3, 2/3, 2/3, 4/3, 5/3], 1/27)/GAMMA(2/3)^4), n=1,2... .
CROSSREFS
KEYWORD
nonn
AUTHOR
Karol A. Penson, Mar 03 2009
STATUS
approved