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A273660 Number of forests of labeled rooted trees of height at most 1, with n labels, ten of which are used for root nodes and any root may contain >= 1 labels.

%I A273660 #4 May 27 2016 12:40:59
%S A273660 115975,6188545,188526162,4324211606,83234980829,1422697691415,
%T A273660 22336690031656,329296289467288,4628083121855622,62687799439000450,
%U A273660 824939949711312292,10611095747493196956,134039591449028959694,1668916223557034160170,20541239452587941670792
%N A273660 Number of forests of labeled rooted trees of height at most 1, with n labels, ten of which are used for root nodes and any root may contain >= 1 labels.
%H A273660 Alois P. Heinz, <a href="/A273660/b273660.txt">Table of n, a(n) for n = 10..986</a>
%F A273660 E.g.f.: x^10/10! * Sum_{j=0..10} Stirling2(10,j)*exp(x)^j.
%F A273660 a(n) = C(n,10) * Sum_{j=0..10} Stirling2(10,j) * j^(n-10).
%p A273660 a:= n-> binomial(n,10)*add(Stirling2(10,j)*j^(n-10), j=0..10):
%p A273660 seq(a(n), n=10..40);
%Y A273660 Column k=10 of A143396.
%K A273660 nonn
%O A273660 10,1
%A A273660 _Alois P. Heinz_, May 27 2016