|
|
A153028
|
|
Special values of the hypergeometric function of the type 4F0.
|
|
2
|
|
|
1, 1, 1, 1, 7, 31, 361, 3361, 57121, 873937, 20110861, 446072221, 13230551071, 394398451591, 14556740314117, 554429787469741, 24799106347186081
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,5
|
|
LINKS
|
|
|
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
|
hypergeom([ -n/2, 1/2-n/2, 1-n/2, 3/2-n/2], [], 4) ;
simplify(%) ;
end proc:
|
|
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
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|