A073306 a(n) = Product_{2i<n} binomial(2*n-2*i-1, 2*i).

1, 1, 1, 3, 10, 105, 1260, 48510, 2162160, 312161850, 52562109600, 28836887379300, 18539497049673600, 38989721014029185400, 96410946507417622080000, 782067521015701609508820000

Offset

0,4

Links

Table of n, a(n) for n=0..15.

Formula

From Vaclav Kotesovec, Oct 27 2017: (Start)

a(n) ~ A^(3/4) * 2^(n^2/2 - n/2 - 1/48) * exp(n/4 - 1/16) / (Gamma(1/4)^(1/2) * Pi^(n/4 - 1/4) * n^(n/4 + 1/16)) if n is even,

a(n) ~ A^(3/4) * Gamma(1/4)^(1/2) * 2^(n^2/2 - n/2 - 13/48) * exp(n/4 - 1/16) / (Pi^(n/4 + 1/2) * n^(n/4 + 1/16)) if n is odd,

where A is the Glaisher-Kinkelin constant A074962.

(End)

Mathematica

Table[Product[Binomial[2n-2i-1, 2i], {i, Floor[(n-1)/2]}], {n, 0, 20}] (* Harvey P. Dale, Nov 29 2011 *)

Prog

(PARI) {a(n) = prod( i=0, (n-1)\2, binomial( 2*n - 2*i - 1, 2*i))}

Crossrefs

a(n)=A055068(n, n).

Sequence in context: A091342 A093454 A048531 * A290557 A034945 A380789

Adjacent sequences: A073303 A073304 A073305 * A073307 A073308 A073309

Keyword

nonn,easy

Author

Michael Somos, Jul 24 2002

Status

approved