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A165970 a(n) = sqrt( superfactorial(4n) / factorial(2n) ). 2
1, 12, 14515200, 420505587390873600000, 6848282921689337839624757371207680000000000, 592617982969061328644755583860005865281724398591341934673920000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n>=5, 2^(12*n)*10^(12*(n - 4)) | a(n). - G. C. Greubel, Apr 18 2016

LINKS

Seiichi Manyama, Table of n, a(n) for n = 0..14

FORMULA

a(n) = sqrt( A000178(4n) / A000142(2n) ) = sqrt(0! * 1! * ... * (2n-1)! * (2n+1)! * (2n+2)! * ... * (4n)!).

a(n) ~ 2^(8*n^2 + 4*n + 1/6) * n^(4*n^2 + n - 1/24) * Pi^n / (A^(1/2) * exp(6*n^2 + n - 1/24)), where A = A074962 = 1.2824271291... is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Jul 10 2015

a(n) = 2^n * Product_{k=1..2*n} (2*k-1)!. - Seiichi Manyama, Jul 05 2019

a(n) = A^(3/2) * exp(-1/8) * 2^(4*n^2 + n - 1/24) * BarnesG(2*n + 3/2) * BarnesG(2*n + 1) / Pi^(n + 1/4), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jul 05 2019

MATHEMATICA

Table[Sqrt[Product[k!, {k, 0, 4*n}]/(2*n)!], {n, 0, 10}] (* Vaclav Kotesovec, Jul 10 2015 *)

PROG

(PARI) {a(n) = 2^n*prod(k=1, 2*n, (2*k-1)!)} \\ Seiichi Manyama, Jul 05 2019

CROSSREFS

Cf. A168467.

Sequence in context: A145745 A175906 A144546 * A285180 A081357 A127708

Adjacent sequences:  A165967 A165968 A165969 * A165971 A165972 A165973

KEYWORD

nonn

AUTHOR

Max Alekseyev, Oct 02 2009

STATUS

approved

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Last modified October 19 09:22 EDT 2021. Contains 348074 sequences. (Running on oeis4.)