The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A208652 Product{i*C(n,i) : 1<=i<=floor[(n+1)/2]}. 4

%I #7 Apr 10 2024 08:02:02

%S 1,2,18,48,3000,10800,4321800,21073920,51849745920,342921600000,

%T 5062554438480000,45444644517888000,3960533401513405516800,

%U 48272757747179554068480,24547182197052103038450000000

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

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

%t m[n_]:=Floor[(n+1)/2];z=21;

%t g[n_]:=Product[i*Binomial[n,i],{i,1,m[n]}]

%t Table[g[n],{n,1,z}] (* A208652 *)

%t 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 *)

%Y Cf. A208653, A208654.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 02 2012

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 27 12:27 EDT 2024. Contains 372858 sequences. (Running on oeis4.)