A208652 Product{i*C(n,i) : 1<=i<=floor[(n+1)/2]}.

1, 2, 18, 48, 3000, 10800, 4321800, 21073920, 51849745920, 342921600000, 5062554438480000, 45444644517888000, 3960533401513405516800, 48272757747179554068480, 24547182197052103038450000000

Offset: 1

Author

Clark Kimberling, Mar 02 2012

Keywords

• nonn

Comments

Used, along with A208653, to count palindromic paths in A208654.

Crossrefs

Cf. A208653, A208654.

Programs

Mathematica

m[n_]:=Floor[(n+1)/2];z=21;
g[n_]:=Product[i*Binomial[n,i],{i,1,m[n]}]
Table[g[n],{n,1,z}] (* A208652 *)
Table[Gamma[1 + n]^(n/2)/BarnesG[1 + n]*((1 + (-1)^n)/2 + (1 - (-1)^n) * Sqrt[Gamma[1 + n]]/(2*Gamma[(1 + n)/2])), {n, 1, 15}] (* Vaclav Kotesovec, Apr 10 2024 *)