A165975 a(n) = sqrt( binomial(4n,0) * binomial(4n,1) * ... * binomial(4n,2n-1) ).

1, 2, 112, 261360, 27983155200, 143829595278720000, 36441048083860298170220544, 463109968103790656729135319264000000, 298869615482782118878970689211942578421760000000

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