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A273658 Number of forests of labeled rooted trees of height at most 1, with n labels, eight of which are used for root nodes and any root may contain >= 1 labels.

%I A273658 #4 May 27 2016 12:31:28
%S A273658 4140,153063,3315645,55239525,786082275,10081916559,120278261103,
%T A273658 1361959159275,14838761544750,157056039953670,1626124163724918,
%U A273658 16555067600440590,166368479811851850,1655233308679110930,16341232769733507570,160366537782578273850
%N A273658 Number of forests of labeled rooted trees of height at most 1, with n labels, eight of which are used for root nodes and any root may contain >= 1 labels.
%H A273658 Alois P. Heinz, <a href="/A273658/b273658.txt">Table of n, a(n) for n = 8..1000</a>
%F A273658 E.g.f.: x^8/8! * Sum_{j=0..8} Stirling2(8,j)*exp(x)^j.
%F A273658 a(n) = C(n,8) * Sum_{j=0..8} Stirling2(8,j) * j^(n-8).
%p A273658 a:= n-> binomial(n,8)*add(Stirling2(8,j)*j^(n-8), j=0..8):
%p A273658 seq(a(n), n=8..40);
%Y A273658 Column k=8 of A143396.
%K A273658 nonn
%O A273658 8,1
%A A273658 _Alois P. Heinz_, May 27 2016