A157643 a(n) arises in the normal ordering of n-th power of the operator (d/dx)^3(x(d/dx))^4

15, 32457, 429687607, 18760111396385, 2007806646217026751, 441585560786152156144665, 177460844217161822403612174167, 119808489676348407935171406661046657

Offset

1,1

Comments

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

In Maple notation:

Links

Table of n, a(n) for n=1..8.

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

Sequence in context: A208461 A068939 A179106 * A340291 A104682 A185902

Adjacent sequences: A157640 A157641 A157642 * A157644 A157645 A157646

Keyword

nonn

Author

Karol A. Penson, Mar 03 2009

Status

approved