A137942 First bisection of A134772.

1, 28, 27165600, 1445549490000000, 1081114481157129619200000, 5873237165016878140678626432000000, 156064894765355001368149078831725782016000000, 15583529649395480761968847415068808311749204480000000000, 4843348111055914672023195506389150149608445774198528000000000000000, 4067688449094150594904537709530563016131839124729830583634193326080000000000000

Offset: 0

Author

N. J. A. Sloane, Oct 18 2009

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..63

Crossrefs

Cf. A134772.

Programs

Magma

B:=Binomial; F:=Factorial;
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]]) >;
[A137942(n): n in [0..30]]; // G. C. Greubel, Oct 16 2023

Mathematica

Table[((8*n)!/(24)^(2*n))*Hypergeometric1F1[-2*n,1/2-4*n,-3/2], {n,0,30}] (* G. C. Greubel, Oct 16 2023 *)

SageMath

b=binomial; f=factorial;
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))
[A137942(n) for n in range(31)] # G. C. Greubel, Oct 16 2023

Formula

From G. C. Greubel, Oct 16 2023: (Start)

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).

a(n) = ((8*n)!/(24)^(2*n))*Hypergeometric1F1([-2*n], [1/2-4*n], -3/2). (End)

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