%I #24 Dec 26 2021 20:59:33

%S 1,1,2,1,8,5,16,7,128,21,256,33,1024,429,2048,715,32768,2431,65536,

%T 4199,262144,29393,524288,52003,4194304,185725,8388608,334305,

%U 33554432,9694845,67108864,17678835,2147483648

%N Numerator of n!!/(n+3)!!.

%D S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996.

%H Robert Israel, <a href="/A004732/b004732.txt">Table of n, a(n) for n = 0..3327</a>

%H S. Janson, <a href="http://www2.math.uu.se/~svante/papers/sj114.pdf">On the traveling fly problem</a>

%F From _Robert Israel_, Jan 07 2019: (Start)

%F a(2*m) = 2^(2*m+1 - A048881(m) - A007814(m+1)).

%F a(2*m+1) = A000265(A000108(m+1)). (End)

%p f:= proc(n) local m,r;

%p m:= floor(n/2);

%p if n::even then 2^(2*m - padic:-ordp(binomial(2*m+1,m),2) - padic:-ordp(m+1,2))

%p else

%p r:= binomial(2*m+2,m+1)/(m+2);

%p r/2^padic:-ordp(r,2);

%p fi

%p end proc:

%p map(f, [$0..50]); # _Robert Israel_, Jan 07 2019

%t Numerator[Table[n!!/(n+3)!!,{n,0,40}]] (* _Harvey P. Dale_, Nov 26 2015 *)

%o (PARI) a(n) = numerator(prod(i=0, floor((n-1)/2), n-2*i)/prod(i=0, floor((n+2)/2), n+3-2*i)) \\ _Michel Marcus_, May 24 2013

%Y Cf. A000108, A000265, A004733, A007814, A048881.

%K nonn,frac

%O 0,3

%A _N. J. A. Sloane_