Search: id:A036069
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%I A036069
%S A036069 1,2,1,4,3,16,5,32,35,256,63,512,231,2048,429,4096,6435,
%T A036069 65536,12155,131072,46189,524288,88179,1048576,676039,8388608,
%U A036069 1300075,16777216,5014575,67108864,9694845,134217728,300540195
%N A036069 Denominator of rational part of Haar measure on Grassmannian space G(n,
               1).
%C A036069 Also rational part of denominator of GAMMA(n/2+1)/GAMMA(n/2+1/2) (cf. 
               A004731).
%D A036069 D. A. Klain and G.-C. Rota, Introduction to Geometric Probability, Cambridge, 
               p. 67.
%e A036069 1, 1, 1/2*Pi, 2, 3/4*Pi, 8/3, 15/16*Pi, 16/5, 35/32*Pi, 128/35, 315/256*Pi, 
               ...
%e A036069 The sequence GAMMA(n/2+1)/GAMMA(n/2+1/2), n >= 0, begins 1/Pi^(1/2), 
               1/2*Pi^(1/2), 2/Pi^(1/2), 3/4*Pi^(1/2), 8/3/Pi^(1/2), 15/16*Pi^(1/
               2), 16/5/Pi^(1/2), ...
%p A036069 if n mod 2 = 0 then k := n/2; 2*k*Pi*binomial(2*k-1,k)/4^k else k := 
               (n-1)/2; 4^k/binomial(2*k,k); fi;
%p A036069 f:=n->simplify(GAMMA(n/2+1)/GAMMA(n/2+1/2));
%Y A036069 Cf. A004731.
%Y A036069 Bisections are A001790 and A101926.
%Y A036069 Cf. A004731, A046161, A001790, A001803, A101926.
%Y A036069 Sequence in context: A099331 A146001 A091879 this_sequence A009477 A105568 
               A004175
%Y A036069 Adjacent sequences: A036066 A036067 A036068 this_sequence A036070 A036071 
               A036072
%K A036069 nonn,easy,nice,frac
%O A036069 0,2
%A A036069 N. J. A. Sloane (njas(AT)research.att.com).

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