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A215860
Number of simple labeled graphs on n nodes with exactly 10 connected components that are trees or cycles.
3
1, 55, 2365, 90805, 3367364, 124984860, 4743643190, 186488038880, 7653850266777, 329429479792985, 14903545528332565, 709243144460040645, 35495878932860944422, 1866637759375098988740, 103014318586612720480259, 5957391569989223921495400
OFFSET
10,2
LINKS
EXAMPLE
a(11) = 55: each graph has one 2-node tree and 9 1-node trees and C(11,2) = 55.
MAPLE
T:= proc(n, k) option remember; `if`(k<0 or k>n, 0,
`if`(n=0, 1, add(binomial(n-1, i)*T(n-1-i, k-1)*
`if`(i<2, 1, i!/2 +(i+1)^(i-1)), i=0..n-k)))
end:
a:= n-> T(n, 10):
seq(a(n), n=10..30);
CROSSREFS
Column k=10 of A215861.
The unlabeled version is A215980.
Sequence in context: A240687 A053113 A012048 * A020536 A212788 A131557
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 26 2012
STATUS
approved