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%I #13 Oct 21 2023 04:27:31
%S 1,28,27165600,1445549490000000,1081114481157129619200000,
%T 5873237165016878140678626432000000,
%U 156064894765355001368149078831725782016000000,15583529649395480761968847415068808311749204480000000000,4843348111055914672023195506389150149608445774198528000000000000000,4067688449094150594904537709530563016131839124729830583634193326080000000000000
%N First bisection of A134772.
%H G. C. Greubel, <a href="/A137942/b137942.txt">Table of n, a(n) for n = 0..63</a>
%F From _G. C. Greubel_, Oct 16 2023: (Start)
%F a(n) = ((8*n)!/(24)^(2*n))*Sum_{j=0..2*n} ( b(2*n, j)*b(4*n, j)*(-6)^j )/( j! * b(2*j, j)*b(8*n, 2*j) ), where b(x,y) = binomial(x,y).
%F a(n) = ((8*n)!/(24)^(2*n))*Hypergeometric1F1([-2*n], [1/2-4*n], -3/2). (End)
%F a(n) ~ sqrt(Pi) * 2^(18*n + 2) * n^(8*n + 1/2) / (3^(2*n) * exp(8*n + 3/4)). - _Vaclav Kotesovec_, Oct 21 2023
%t Table[((8*n)!/(24)^(2*n))*Hypergeometric1F1[-2*n,1/2-4*n,-3/2], {n,0,30}] (* _G. C. Greubel_, Oct 16 2023 *)
%o (Magma)
%o B:=Binomial; F:=Factorial;
%o A137942:= func< n | F(8*n)/(24)^(2*n)*(&+[B(2*n, j)*B(4*n, j)*(-6)^j/(F(j)*B(2*j, j)*B(8*n, 2*j)) : j in [0..2*n]]) >;
%o [A137942(n): n in [0..30]]; // _G. C. Greubel_, Oct 16 2023
%o (SageMath)
%o b=binomial; f=factorial;
%o def A137942(n): return (f(8*n)/(24)^(2*n))*sum(b(2*n,j)*b(4*n,j)*(-6)^j/(f(j)*b(2*j,j)*b(8*n,2*j)) for j in range(2*n+1))
%o [A137942(n) for n in range(31)] # _G. C. Greubel_, Oct 16 2023
%Y Cf. A134772.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Oct 18 2009
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