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A215851
Number of simple labeled graphs on n nodes with exactly 1 connected component that is a tree or a cycle.
3
1, 1, 4, 19, 137, 1356, 17167, 264664, 4803129, 100181440, 2359762091, 61937322624, 1792399894837, 56697025885696, 1946238657504975, 72058247875111936, 2862433512904759793, 121439708940308299776, 5480390058971655049939, 262144060822550204416000
OFFSET
1,3
LINKS
FORMULA
a(1) = a(2) = 1, a(n) = A000272(n) + A001710(n-1) = n^(n-2) + (n-1)!/2 for n>2.
EXAMPLE
a(3) = 4:
.1-2. .1-2. .1-2. .1 2.
.|/ . .| . . / . .|/ .
.3... .3... .3... .3...
MAPLE
a:= n-> `if`(n<3, 1, (n-1)!/2+n^(n-2)):
seq(a(n), n=1..25);
CROSSREFS
Column k=1 of A215861.
The unlabeled version is A215981.
Sequence in context: A157303 A007788 A259354 * A197920 A208811 A305725
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Aug 25 2012
STATUS
approved