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COMMENT
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Special values of a sum of two hypergeometric functions of type 3F4.
In Maple notation:
a(n)=2^(3*n-1)*exp(-1)*((n!)^3*hypergeom([n+1,n+1,n+1],[1,1,3/2,2],1/4)+
2*(GAMMA(n+1/2)/sqrt(Pi))^3*hypergeom([n+1/2,n+1/2,n+1/2],[1/2,1/2,1/2,3/2],1/4)), n=1,2... .
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