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A273654 Number of forests of labeled rooted trees of height at most 1, with n labels, four of which are used for root nodes and any root may contain >= 1 labels.

%I A273654 #5 May 27 2016 12:05:37
%S A273654 15,185,1485,9905,59850,341082,1872990,10032990,52814025,274436305,
%T A273654 1411449039,7195628895,36390053700,182622509860,909578754540,
%U A273654 4496410556268,22062707386875,107464431586995,519700280676885,2495827315731365,11905791978208590,56429414876395550
%N A273654 Number of forests of labeled rooted trees of height at most 1, with n labels, four of which are used for root nodes and any root may contain >= 1 labels.
%H A273654 Alois P. Heinz, <a href="/A273654/b273654.txt">Table of n, a(n) for n = 4..1000</a>
%F A273654 E.g.f.: x^4/4! * Sum_{j=0..4} Stirling2(4,j)*exp(x)^j.
%F A273654 a(n) = C(n,4) * Sum_{j=0..4} Stirling2(4,j) * j^(n-4).
%p A273654 a:= n-> binomial(n,4)*add(Stirling2(4,j)*j^(n-4), j=0..4):
%p A273654 seq(a(n), n=4..40);
%Y A273654 Column k=4 of A143396.
%K A273654 nonn
%O A273654 4,1
%A A273654 _Alois P. Heinz_, May 27 2016