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a(n) arises in the normal ordering of n-th power of the operator (d/dx)^3(x(d/dx))^4
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%I #2 Mar 30 2012 18:49:55

%S 15,32457,429687607,18760111396385,2007806646217026751,

%T 441585560786152156144665,177460844217161822403612174167,

%U 119808489676348407935171406661046657

%N a(n) arises in the normal ordering of n-th power of the operator (d/dx)^3(x(d/dx))^4

%C Special values of a sum of three hypergeometric functions of type 4F6.

%C In Maple notation:

%F a(n)=exp(-1)*3^(4*n)*((1/6)*(n!)^4*hypergeom([n+1, n+1, n+1, n+1],

%F [1, 1, 1, 4/3, 5/3, 2], 1/27)+(9/16)*GAMMA(2/3)^4*GAMMA(n+1/3)^4

%F *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],

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

%F , [2/3, 2/3, 2/3, 2/3, 4/3, 5/3], 1/27)/GAMMA(2/3)^4), n=1,2... .

%K nonn

%O 1,1

%A _Karol A. Penson_, Mar 03 2009