A038095 Number of rooted connected graphs on n labeled nodes where the root has degree 2.

6, 72, 1440, 49680, 2998800, 324237312, 64440883584, 24059497893120, 17143668999705600, 23569875858252303360, 63000019679242001900544, 329150325651711743768150016, 3374625529825460904919664793600, 68094821953233373962606732799672320

Offset: 3

Author

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

Keywords

• nonn
• easy

Links

• Andrew Howroyd, Table of n, a(n) for n = 3..50

Crossrefs

Cf. A038094, A038096, A038097.

Programs

PARI

seq(n)={Vec(serlaplace(sum(k=1, n, k*binomial(k-1, 2)*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 resp E.g.f.'s of A038094 and A006125.

Extensions

Terms a(12) and beyond corrected by Andrew Howroyd, Nov 23 2020