A208649 (1/n)*A073617(n+1).

1, 1, 1, 3, 6, 40, 150, 2100, 14700, 423360, 5556600, 325987200, 8068183200, 958961203200, 44996257706400, 10799101849536000, 965169727802280000, 466713183932835840000, 79775138681769651120000

Offset: 1

Author

Clark Kimberling, Feb 29 2012

Keywords

• nonn

Crossrefs

Cf. A073617.

Programs

Mathematica

p[n_] := Product[Binomial[n + 1 - k, k],
 {k, 1, Floor[(n + 1)/2]}]
Table[p[n], {n, 1, 20}]   (* A073617(n+1) *)
Table[p[n]/n, {n, 1, 20}] (* A208649 *)

Formula

a(n) ~ A^(3/2) * 2^((n*(n+3))/4 + 1/3 - (-1)^n/4) * exp(n/4 - 1/8) / (n^(n/4 + 3/2 - (-1)^n/8) * Pi^(n/4 + (5 - (-1)^n)/8)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jun 10 2025