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%I #4 May 27 2016 11:40:54
%S 5,40,220,1040,4550,19040,77448,308640,1209450,4668400,17766892,
%T 66718288,247397150,906584000,3285842960,11788924992,41902786770,
%U 147668053200,516315206260,1792304871280,6180666260230,21184488791840,72205377800600,244837696095200
%N Number of forests of labeled rooted trees of height at most 1, with n labels, three of which are used for root nodes and any root may contain >= 1 labels.
%H Alois P. Heinz, <a href="/A273653/b273653.txt">Table of n, a(n) for n = 3..1000</a>
%F E.g.f.: x^3/3! * Sum_{j=0..3} Stirling2(3,j)*exp(x)^j.
%F a(n) = C(n,3) * Sum_{j=0..3} Stirling2(3,j) * j^(n-3).
%p a:= n-> binomial(n,3)*add(Stirling2(3,j)*j^(n-3), j=0..3):
%p seq(a(n), n=3..40);
%Y Column k=3 of A143396.
%K nonn
%O 3,1
%A _Alois P. Heinz_, May 27 2016