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 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

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