A215773 Number of undirected labeled graphs on n+3 nodes with exactly n cycle graphs as connected components.

0, 3, 25, 120, 420, 1190, 2898, 6300, 12540, 23265, 40755, 68068, 109200, 169260, 254660, 373320, 534888, 750975, 1035405, 1404480, 1877260, 2475858, 3225750, 4156100, 5300100, 6695325, 8384103, 10413900, 12837720, 15714520, 19109640, 23095248, 27750800

Offset

0,2

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Formula

G.f.: (8*x^2+4*x+3)*x/(1-x)^7.

a(n) = n*(n+1)*(n+2)*(n+3)*(n^2+n+4)/48.

Example

a(1) = 3:  .1-2.  .1.2.  .1-2.
.          .|.|.  .|X|.  ..X..
.          .3-4.  .3.4.  .3-4.

Maple

a:= n-> (24+(50+(41+(21+(7+n)*n)*n)*n)*n)*n/48:
seq (a(n), n=0..40);

Crossrefs

A diagonal of A215771.

Sequence in context: A059457 A165206 A095664 * A099868 A243228 A112495

Adjacent sequences: A215770 A215771 A215772 * A215774 A215775 A215776

Keyword

nonn

Author

Alois P. Heinz, Aug 23 2012

Status

approved