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%I #17 May 17 2018 09:14:46
%S 1,2,3,6,50,100,1794,3588,114840,229680,11483880,22967760,1653679440,
%T 3307358880,324121165200,648242330400,82975018331520,165950036663040,
%U 26883905939049600,53767811878099200,10753562375623468800,21507124751246937600,5204724189801718982400
%N a(n) = 2^n*floor(n/2)!*Gamma(ceiling((n+1)/2),-1/4)*exp(-1/4).
%H G. C. Greubel, <a href="/A277374/b277374.txt">Table of n, a(n) for n = 0..445</a>
%F a(n) ~ Pi*exp(-1/4-n)*n^(n+1) if n is even, a(n) ~ 2*Pi*exp(3/4-n)*(n-1)^n if n is odd. - _Vladimir Reshetnikov_, Oct 19 2016
%p a := n -> 2^n*floor(n/2)!*GAMMA(ceil((n+1)/2),-1/4)*exp(-1/4):
%p seq(simplify(a(n)),n=0..22);
%t a[n_] := 2^n Floor[n/2]! Gamma[Ceiling[(1 + n)/2],-1/4] Exp[-1/4];
%t FunctionExpand@Table[a[n], {n,0,22}]
%o (PARI) for(n=0, 20, print1(round(2^n*(floor(n/2))!*exp(-1/4)* incgam(ceil((n +1)/2), -1/4)), ", ")) \\ _G. C. Greubel_, May 16 2018
%Y a(n) * A056040(n) = A277393(n).
%K nonn
%O 0,2
%A _Peter Luschny_, Oct 17 2016