A153028 Special values of the hypergeometric function of the type 4F0.

1, 1, 1, 1, 7, 31, 361, 3361, 57121, 873937, 20110861, 446072221, 13230551071, 394398451591, 14556740314117, 554429787469741, 24799106347186081

Offset

0,5

Links

Table of n, a(n) for n=0..16.

Formula

In Maple notation, a(n)=hypergeom([ -n/2,1/2-n/2,1-n/2,3/2-n/2],[],4), n=0,1... .

a(n) ~ 2^(-n/2 - 5/8) * exp(2^(5/4) * n^(1/4) - 3*n/2) * n^(3*n/2 - 9/8) * (1 - 15/(16*2^(1/4)*n^(1/4)) - 151/(512*sqrt(2*n)) + 4155/(8192*2^(3/4)*n^(3/4))). - Vaclav Kotesovec, Jul 05 2018

D-finite with recurrence 4*a(n) -4*a(n-1) -4*(n-1)*(n-2)*(n-3)*a(n-2) +(n-5)*(n-1)*(n-2)*(n-4)*(n-3)^2*a(n-4)=0. - R. J. Mathar, Jul 27 2022

Maple

A153028 := proc(n)
        hypergeom([ -n/2, 1/2-n/2, 1-n/2, 3/2-n/2], [], 4) ;
        simplify(%) ;
end proc:
seq(A153028(n), n=0..60) ; # R. J. Mathar, Jul 27 2022

Mathematica

Table[HypergeometricPFQ[{-n/2, 1/2-n/2, 1-n/2, 3/2-n/2}, {}, 4], {n, 0, 20}] (* Vaclav Kotesovec, Jul 05 2018 *)

Crossrefs

Sequence in context: A344787 A253596 A298958 * A276667 A322894 A232993

Adjacent sequences: A153025 A153026 A153027 * A153029 A153030 A153031

Keyword

nonn

Author

Karol A. Penson, Dec 17 2008

Status

approved