A215851 Number of simple labeled graphs on n nodes with exactly 1 connected component that is a tree or a cycle.

1, 1, 4, 19, 137, 1356, 17167, 264664, 4803129, 100181440, 2359762091, 61937322624, 1792399894837, 56697025885696, 1946238657504975, 72058247875111936, 2862433512904759793, 121439708940308299776, 5480390058971655049939, 262144060822550204416000

Offset

1,3

Links

Alois P. Heinz, Table of n, a(n) for n = 1..150

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.

Cf. A000272, A001710.

Sequence in context: A157303 A007788 A259354 * A197920 A208811 A305725

Adjacent sequences: A215848 A215849 A215850 * A215852 A215853 A215854

Keyword

nonn

Author

Alois P. Heinz, Aug 25 2012

Status

approved