A329928 - OEIS

%I #8 Dec 05 2019 15:09:13

%S 2,32,2048,294912,75497472,30198988800,17394617548800,

%T 13637380158259200,13964677282057420800,18098221757546417356800,

%U 28957154812074267770880000,56061051716175782404423680000,129164663154069002659792158720000,349261249168602583192077997178880000

%N a(n) = (Pi/2)*(2*n+1)!*binomial(2*n+1, (2*n+1)/2).

%F a(n) = 2^(4*n + 1)*Gamma(n + 1)^2.

%F a(n) = a(n-1)*(4*n)^2 for n > 0.

%p a := proc(n) option remember; if n = 0 then 2 else 16*a(n-1)*n^2 fi end:

%p seq(a(n), n = 0..13);

%o (PARI) \p100; binom(n,k)=gamma(n+1)/(gamma(k+1)*gamma(n-k+1));

%o for(n=0,14,print1(round((Pi/2)*(2*n+1)!*binom(2*n+1,(2*n+1)/2)),", ")) \\ _Hugo Pfoertner_, Dec 05 2019

%K nonn

%O 0,1

%A _Peter Luschny_, Dec 05 2019