%I #6 Mar 31 2012 14:02:17
%S 1,1,2,3,8,24,72,231,764,2574,8840,30796,108528,386308,1386756,
%T 5014575,18249120,66786738,245642760,907513530,3366215688,12531502620,
%U 46805032560,175341580596,658674458208,2480584898700,9363748625972
%N Number of cycles in range [A014137(n-1)..A014138(n-1)] of permutation A089851/A089853.
%C The number of orbits to which the corresponding automorphism(s) partitions the set of A000108(n) binary trees with n internal nodes.
%H A. Karttunen, <a href="/A089408/a089408.c.txt">C-program for computing the initial terms of this sequence</a>
%F a(n) = (1/3 * A000108(n)) + (2/3 * A089848(n))
%p A089847 := n -> (1/3)*(A000108(n)+2*A089848(n));
%o (Scheme) (define (A089847 n) (/ (+ (A000108 n) (* 2 (A089848 n))) 3))
%K nonn,easy
%O 0,3
%A _Antti Karttunen_, Nov 29 2003