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%I #4 Mar 30 2012 18:37:42
%S 1,1,2,1,3,4,1,4,7,10,1,5,12,22,26,1,6,19,43,66,80,1,7,26,73,143,217,
%T 246,1,8,35,116,273,504,715,810,1,9,46,172,476,1038,1768,2438,2704,1,
%U 10,57,245,776,1944,3876,6310,8398,9252,1,11,70,335,1197,3399,7752
%N Triangle giving T(n,m) = number of necklaces of two colors with 2n beads of which m=1..n are black.
%C Left half of even rows of triangle A047996 (with the leftmost edge discarded).
%F (1/(2n)) Sum_{d |(2n, m)} phi(d)*binomial(2n/d, m/d)
%t Table[(Plus@@(EulerPhi[ # ]Binomial[2n/#, m/# ] &)/@Intersection[Divisors[2n], Divisors[m]])/(2n), {n, 13}, {m, n}]
%Y Penultimate entries give binary necklaces of n-1 black beads and n+1 white beads, presumably A007595, antepenultimate entries give binary necklaces of n-2 black beads and n+2 white beads, presumably A003444.
%Y Cf. A047996, A003444.
%K nonn,tabl
%O 1,3
%A _Wouter Meeussen_, Aug 03 2002
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