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A120248
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a(n) = Product_{k=0..n} C(n+k+2, n+2).
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2
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1, 4, 75, 7056, 3457440, 9032601600, 127843321480875, 9917120529316000000, 4253520573615071657074176, 10156681309872614660803421798400, 135766978921156343322148046967386880000, 10205737152660536205131284348877857357824000000
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OFFSET
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0,2
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COMMENTS
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Divisors in number triangle A120247.
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LINKS
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FORMULA
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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
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MATHEMATICA
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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 *)
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PROG
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(Magma)
A120248:= func< n | (&*[Binomial(n+j+2, n+2): j in [0..n]]) >;
(SageMath)
def A120248(n): return product( binomial(n+j+2, n+2) for j in range(n+1))
(PARI) a(n) = prod(k=0, n, binomial(n+k+2, n+2)); \\ Michel Marcus, Mar 16 2023
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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