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Denominator of average distance traveled by n-dimensional fly.
2

%I #19 Oct 26 2023 08:42:20

%S 1,3,4,15,8,35,64,315,128,693,512,3003,1024,6435,16384,109395,32768,

%T 230945,131072,969969,262144,2028117,2097152,16900975,4194304,

%U 35102025,16777216,145422675,33554432

%N Denominator 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) = denominator(d(n)) if n is odd and a(n) = denominator(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>.

%F a(2n) = A001803(n) (conjectured). - _Ralf Stephan_, Mar 10 2004

%o (PARI) a(n) = {if (n % 2, eo = 2, eo = 4); denominator(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. A004734.

%K nonn,frac

%O 1,2

%A _N. J. A. Sloane_