A215863 Number of simple labeled graphs on n+3 nodes with exactly n connected components that are trees or cycles.

0, 19, 135, 540, 1610, 3990, 8694, 17220, 31680, 54945, 90805, 144144, 221130, 329420, 478380, 679320, 945744, 1293615, 1741635, 2311540, 3028410, 3920994, 5022050, 6368700, 8002800, 9971325, 12326769, 15127560, 18438490, 22331160, 26884440, 32184944, 38327520

Offset: 0

Author

Alois P. Heinz, Aug 25 2012

Keywords

• nonn

Examples

			a(1) = 19:
.1-2.  .1-2.  .1 2.  .1-2.  .1-2.  .1 2.  .1 2.  .1 2.  .1-2.  .1-2.
.| |.  . X .  .|X|.  .|\ .  . /|.  . \|.  .|/ .  .| |.  .|  .  .| |.
.4-3.  .4-3.  .4.3.  .4.3.  .4.3.  .4-3.  .4-3.  .4-3.  .4-3.  .4.3.
.
.1-2.  .1 2.  .1-2.  .1-2.  .1-2.  .1 2.  .1 2.  .1 2.  .1 2.
.  |.  . X .  . / .  . \ .  . X .  .|/|.  . X|.  .|X .  .|\|.
.4-3.  .4-3.  .4-3.  .4-3.  .4.3.  .4.3.  .4.3.  .4.3.  .4.3.
		

Links

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

Crossrefs

A diagonal of A215861.

Programs

Maple

a:= n-> binomial(n+3,4)*(24+(13+n)*n)/2:
seq(a(n), n=0..40);

Formula

G.f.: (6*x^2-2*x-19)*x/(x-1)^7.

a(n) = C(n+3,4)*(n^2+13*n+24)/2.