A120248 a(n) = Product_{k=0..n} C(n+k+2, n+2).

1, 4, 75, 7056, 3457440, 9032601600, 127843321480875, 9917120529316000000, 4253520573615071657074176, 10156681309872614660803421798400, 135766978921156343322148046967386880000, 10205737152660536205131284348877857357824000000

Offset: 0

Author

Paul Barry, Jun 12 2006

Keywords

• easy
• nonn

Comments

Divisors in number triangle A120247.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..50

Crossrefs

Cf. A120247.

Programs

Magma

A120248:= func< n | (&*[Binomial(n+j+2, n+2): j in [0..n]]) >;
[A120248(n): n in [0..20]]; // G. C. Greubel, Mar 16 2023

Mathematica

Table[Gamma[n+2]*BarnesG[2*n+4]/((Gamma[n+3])^(n-1)*BarnesG[n+4]^2), {n,0,20}] (* G. C. Greubel, Mar 16 2023 *)

PARI

a(n) = prod(k=0, n, binomial(n+k+2, n+2)); \\ Michel Marcus, Mar 16 2023

SageMath

def A120248(n): return product( binomial(n+j+2, n+2) for j in range(n+1))
[A120248(n) for n in range(21)] # G. C. Greubel, Mar 16 2023

Formula

a(n) = Gamma(n+2)*BarnesG(2*n+4)/((Gamma(n+3))^(n-1)*BarnesG(n+4)^2). - G. C. Greubel, Mar 16 2023

a(n) ~ A * 2^(47/12 + 11*n/2 + 2*n^2) / (exp(19/6 + 2*n + n^2/2) * Pi^((n+1)/2) * n^(5/12 + n/2)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Aug 29 2023