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%I #10 Jul 29 2022 16:45:59
%S 1,1,1,1,7,31,361,3361,57121,873937,20110861,446072221,13230551071,
%T 394398451591,14556740314117,554429787469741,24799106347186081
%N Special values of the hypergeometric function of the type 4F0.
%F In Maple notation, a(n)=hypergeom([ -n/2,1/2-n/2,1-n/2,3/2-n/2],[],4), n=0,1... .
%F 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
%F 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
%p A153028 := proc(n)
%p hypergeom([ -n/2,1/2-n/2,1-n/2,3/2-n/2],[],4) ;
%p simplify(%) ;
%p end proc:
%p seq(A153028(n),n=0..60) ; # _R. J. Mathar_, Jul 27 2022
%t Table[HypergeometricPFQ[{-n/2,1/2-n/2,1-n/2,3/2-n/2},{},4], {n,0,20}] (* _Vaclav Kotesovec_, Jul 05 2018 *)
%K nonn
%O 0,5
%A _Karol A. Penson_, Dec 17 2008
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