|
%I #9 May 13 2013 17:12:51
%S 0,2,12,90,864,10290,147456,2480058,48000000,1052307234,25798901760,
%T 699896958618,20826335158272,674680957031250,23643898043695104,
%U 891412022961534330,35982083287879778304,1548474957047229426498,70778880000000000000000
%N Number of trees over all forests of labeled rooted trees in which some (possibly all or none) of the trees have been specially designated.
%C The expected number of trees in each such forest a(n)/A089140(offset) approaches 3 as n gets large.
%F a(n) = Sum_{k=0..n} binomial(n-1,k-1)*n^(n-k)*2^k*k = 6*n*(n+2)^(n-2).
%t nn = 18; tx = Sum[n^(n - 1) x^n/n!, {n, 1, nn}]; Range[0, nn]! CoefficientList[Series[D[Exp[y tx]^2, y] /. y -> 1, {x, 0, nn}], x]
%Y Cf. A225497.
%K nonn
%O 0,2
%A _Geoffrey Critzer_, May 10 2013
|
