A205825 a(n) = n!/ceiling(n/2)!.

1, 1, 2, 3, 12, 20, 120, 210, 1680, 3024, 30240, 55440, 665280, 1235520, 17297280, 32432400, 518918400, 980179200, 17643225600, 33522128640, 670442572800, 1279935820800, 28158588057600, 53970627110400, 1295295050649600, 2490952020480000, 64764752532480000

Offset: 0

Author

Clark Kimberling, Feb 01 2012

Keywords

• nonn

Crossrefs

Cf. A205785, A205786.

Programs

Mathematica

Table[n!/Ceiling[n/2]!,{n,0,24}]

Formula

E.g.f.: (exp(x^2)*(x+1) -1)/x. - Sergei N. Gladkovskii, Oct 10 2012

Sum_{n>=0} 1/a(n) = 3/2 + 5*exp(1/4)*sqrt(Pi)*erf(1/2)/4, where erf is the error function. - Amiram Eldar, Feb 13 2023

Extensions

a(0)=1 prepended and e.g.f. edited by Alois P. Heinz, Sep 08 2015