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Numerator of average distance traveled by n-dimensional fly.
1

%I #17 Oct 26 2023 08:42:14

%S 1,8,3,32,5,64,35,512,63,1024,231,4096,429,8192,6435,131072,12155,

%T 262144,46189,1048576,88179,2097152,676039,16777216,1300075,33554432,

%U 5014575,134217728,9694845,268435456,300540195

%N Numerator of average distance traveled by n-dimensional fly.

%C The average distance is actually d(n) = 2*n!!/(n+1)!! if n is odd, and d(n) = (1*Pi)*4*n!!/(n+1)!! if n is even. So a(n) = numerator(d(n)) if n is odd and a(n) = numerator(Pi*d(n)) if n is even. - _Michel Marcus_, May 24 2013

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

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

%o (PARI) a(n) = {if (n % 2, eo = 2, eo = 4); numerator(eo*prod(i=0, floor((n-1)/2), n-2*i)/prod(i=0, floor(n/2), n+1-2*i));} \\ _Michel Marcus_, May 24 2013

%Y Cf. A004735.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_