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A215860 Number of simple labeled graphs on n nodes with exactly 10 connected components that are trees or cycles.

%I A215860 #9 Dec 04 2014 07:00:54
%S A215860 1,55,2365,90805,3367364,124984860,4743643190,186488038880,
%T A215860 7653850266777,329429479792985,14903545528332565,709243144460040645,
%U A215860 35495878932860944422,1866637759375098988740,103014318586612720480259,5957391569989223921495400
%N A215860 Number of simple labeled graphs on n nodes with exactly 10 connected components that are trees or cycles.
%H A215860 Alois P. Heinz, <a href="/A215860/b215860.txt">Table of n, a(n) for n = 10..150</a>
%e A215860 a(11) = 55: each graph has one 2-node tree and 9 1-node trees and C(11,2) = 55.
%p A215860 T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
%p A215860       `if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
%p A215860       `if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
%p A215860     end:
%p A215860 a:= n-> T(n, 10):
%p A215860 seq(a(n), n=10..30);
%Y A215860 Column k=10 of A215861.
%Y A215860 The unlabeled version is A215980.
%K A215860 nonn
%O A215860 10,2
%A A215860 _Alois P. Heinz_, Aug 26 2012