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A157642 a(n) arises in the normal ordering of n-th power of the operator (d/dx)^3(x(d/dx))^3 0
5, 1211, 1177071, 2851057633, 13702497878021, 114142446044738995, 1506157186706580123591, 29520950676106077642732801, 818899164643659779062878378373, 30959918834233822075763618062253451 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Special values of a sum of three hypergeometric functions of type 3F5.

In Maple notation:

LINKS

Table of n, a(n) for n=1..10.

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

Sequence in context: A317374 A189249 A034864 * A234811 A069642 A182345

Adjacent sequences:  A157639 A157640 A157641 * A157643 A157644 A157645

KEYWORD

nonn

AUTHOR

Karol A. Penson, Mar 03 2009

STATUS

approved

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Last modified November 17 00:08 EST 2019. Contains 329209 sequences. (Running on oeis4.)