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

1,2

Comments

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

Links

Table of n, a(n) for n=1..15.

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 *)

Crossrefs

Cf. A208653, A208654.

Sequence in context: A126909 A139268 A052681 * A223469 A048910 A356712

Adjacent sequences: A208649 A208650 A208651 * A208653 A208654 A208655

Keyword

nonn

Author

Clark Kimberling, Mar 02 2012

Status

approved