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

3,1

Links

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

Formula

E.g.f.: B(x)/C(x) where B, C resp E.g.f.'s of A038094 and A006125.

Prog

(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

Crossrefs

Cf. A038094, A038096, A038097.

Sequence in context: A089252 A052730 A010796 * A012242 A138446 A099029

Adjacent sequences: A038092 A038093 A038094 * A038096 A038097 A038098

Keyword

nonn,easy

Author

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

Extensions

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

Status

approved