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A165975 a(n) = sqrt( binomial(4n,0) * binomial(4n,1) * ... * binomial(4n,2n-1) ). 2
1, 2, 112, 261360, 27983155200, 143829595278720000, 36441048083860298170220544, 463109968103790656729135319264000000, 298869615482782118878970689211942578421760000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..25

FORMULA

a(n) = (4n)!^n / A165970(n).

a(n) ~ A^(1/2) * exp(2*n^2 + n - 1/48) / (2^(5*n/2 + 1/6) * Pi^(n/2) * n^(n/2 - 1/24)), where A = A074962 is the Glaisher-Kinkelin constant. - Vaclav Kotesovec, Apr 19 2016

MATHEMATICA

Table[Sqrt[Product[Binomial[4*n, k], {k, 0, 2*n - 1}]], {n, 0, 5}] (* G. C. Greubel, Apr 19 2016 *)

PROG

(PARI) a(n) = sqrtint(prod(k=0, 2*n-1, binomial(4*n, k))); \\ Michel Marcus, Apr 19 2016

CROSSREFS

Cf. A262261.

Sequence in context: A024342 A225333 A012525 * A051590 A091302 A209611

Adjacent sequences:  A165972 A165973 A165974 * A165976 A165977 A165978

KEYWORD

nonn

AUTHOR

Max Alekseyev, Oct 02 2009

STATUS

approved

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Last modified May 25 11:27 EDT 2020. Contains 334592 sequences. (Running on oeis4.)