A157281 a(n) arises in the normal ordering of n-th power of the operator (d/dx)^2(x(d/dx))^3.

5, 735, 388495, 481590401, 1137296646141, 4516854024385855, 27752662708200238775, 248444078372890409312385, 3097105045238321286477572341, 51894055293560470969321661603231

Offset

0,1

Comments

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... .

Links

Table of n, a(n) for n=0..9.

Mathematica

Round[Table[(2^(-1 + 3*n)*((2*Gamma[1/2 + n]^3 * HypergeometricPFQ[{1/2 + n, 1/2 + n, 1/2 + n}, {1/2, 1/2, 1/2, 3/2}, 1/4])/Pi^(3/2) + n!^3*HypergeometricPFQ[{1 + n, 1 + n, 1 + n}, {1, 1, 3/2, 2}, 1/4]))/E, {n, 1, 12}]] (* Vaclav Kotesovec, Jun 08 2021 *)

Crossrefs

Cf. A088466.

Sequence in context: A199089 A345357 A260481 * A171269 A172890 A332175

Adjacent sequences: A157278 A157279 A157280 * A157282 A157283 A157284

Keyword

nonn

Author

Karol A. Penson, Mar 03 2009

Status

approved