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

4,1

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A038094, A038095, A038096.

Sequence in context: A159360 A249392 A114933 * A208267 A184758 A189956

Adjacent sequences: A038094 A038095 A038096 * A038098 A038099 A038100

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved