A038097 Number of rooted connected graphs on n labeled nodes where the root has degree 3.

32, 1120, 53760, 4155200, 550305280, 129990260736, 56369709634560, 45808126727193600, 70779622448719134720, 210103333009795315650560, 1207180278201294640467288064, 13500153139563947729371140096000, 295095590701444457972767937903329280

Offset: 4

Author

Christian G. Bower, Jan 04 1999; suggested by Vlady Ravelomanana

Keywords

• nonn
• easy

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. A038094, A038095, A038096.

Programs

PARI

seq(n)={Vec(serlaplace(sum(k=1, n, k*binomial(k-1,3)*2^binomial(k-1,2)*x^k/k!)/sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)))} \\ Andrew Howroyd, Nov 23 2020

Formula

E.g.f.: B(x)/C(x) where B, C respectively are the e.g.f.'s for A038096 and A006125.

Extensions

Terms a(13) and beyond corrected by Andrew Howroyd, Nov 23 2020