This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004734 #17 Oct 26 2023 08:42:14 %S A004734 1,8,3,32,5,64,35,512,63,1024,231,4096,429,8192,6435,131072,12155, %T A004734 262144,46189,1048576,88179,2097152,676039,16777216,1300075,33554432, %U A004734 5014575,134217728,9694845,268435456,300540195 %N A004734 Numerator of average distance traveled by n-dimensional fly. %C A004734 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 A004734 S. Janson, On the traveling fly problem, Graph Theory Notes of New York, Vol. XXXI, 17, 1996. %H A004734 S. Janson, <a href="http://www2.math.uu.se/~svante/papers/sj114.pdf">On the traveling fly problem</a>. %o A004734 (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 A004734 Cf. A004735. %K A004734 nonn,frac %O A004734 1,2 %A A004734 _N. J. A. Sloane_