A038096 Number of rooted graphs on n labeled nodes where the root has degree 3.

32, 1280, 61440, 4587520, 587202560, 135291469824, 57724360458240, 46443371157258240, 71337018097548656640, 211030752203237270487040, 1210134745434243803880882176, 13518305228996352601898436526080

Offset: 4

Author

Christian G. Bower, Jan 04 1999

Keywords

• nonn
• easy

Comments

The graphs are not necessarily connected. The nodes are labeled.

Examples

			For n=4, take 4 nodes labeled a,b,c,d. We can choose the root in 4 ways, say a, and it must be joined to b,c,d. Each of the three edges bc, bd, cd may or may not exist, so there are 4*8 = 32 = a(4) possibilities.
		

Links

• Andrew Howroyd, Table of n, a(n) for n = 4..50

Crossrefs

Cf. A006125, A038094, A038095, A038097.

Programs

Mathematica

Table[n Binomial[n-1,3] 2^Binomial[n-1,2],{n,4,20}] (* Harvey P. Dale, Sep 14 2011 *)

PARI

a(n) = {n*binomial(n-1,3)*2^binomial(n-1,2)} \\ Andrew Howroyd, Nov 23 2020

Formula

a(n) = n*binomial(n-1,3)*2^binomial(n-1,2). (There are n choices for the root, binomial(n-1,3) choices for the nodes it joined to, and 2^binomial(n-1,2) choices for the edges between the non-root nodes.)

Extensions

Edited by N. J. A. Sloane, Sep 14 2011