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%I #10 Dec 16 2014 14:07:28
%S 1,1,3,6,13,26,55,112,238,510,1117,2498,5712,13322,31643,76455,187382,
%T 465393,1168966,2966298,7594035,19597653,50933434,133224112,350477003,
%U 926855665,2462830565,6572892862,17612586165,47369774428,127841265076,346120109957
%N Number of simple unlabeled graphs on n nodes with exactly 5 connected components that are trees or cycles.
%H Alois P. Heinz, <a href="/A215985/b215985.txt">Table of n, a(n) for n = 5..650</a>
%e a(7) = 3: .o-o o o. .o-o o o. .o o o o.
%e .|/ . .| . .| | .
%e .o o o . .o o o . .o o o .
%p with(numtheory):
%p b:= proc(n) option remember; local d, j; `if`(n<=1, n,
%p (add(add(d*b(d), d=divisors(j)) *b(n-j), j=1..n-1))/(n-1))
%p end:
%p g:= proc(n) option remember; local k; `if`(n>2, 1, 0)+ b(n)-
%p (add(b(k)*b(n-k), k=0..n) -`if`(irem(n, 2)=0, b(n/2), 0))/2
%p end:
%p p:= proc(n, i, t) option remember; `if`(n<t, 0, `if`(n=t, 1,
%p `if`(min(i, t)<1, 0, add(binomial(g(i)+j-1, j)*
%p p(n-i*j, i-1, t-j), j=0..min(n/i,t)))))
%p end:
%p a:= n-> p(n, n, 5):
%p seq(a(n), n=5..40);
%Y Column k=5 of A215977.
%Y The labeled version is A215855.
%K nonn
%O 5,3
%A _Alois P. Heinz_, Aug 29 2012
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