%I
%S 6,72,1440,49680,2998800,324237312,64440883584,24059497893120,
%T 17143668999705600,23569875858252303360,63000019679242001900544,
%U 329150325651711743768150016,3374625529825460904919664793600,68094821953233373962606732799672320
%N Number of rooted connected graphs on n labeled nodes where the root has degree 2.
%H Andrew Howroyd, <a href="/A038095/b038095.txt">Table of n, a(n) for n = 3..50</a>
%F E.g.f.: B(x)/C(x) where B, C resp E.g.f.'s of A038094 and A006125.
%o (PARI) seq(n)={Vec(serlaplace(sum(k=1, n, k*binomial(k1, 2)*2^binomial(k1, 2)*x^k/k!)/sum(k=0, n, 2^binomial(k, 2)*x^k/k!) + O(x*x^n)))} \\ _Andrew Howroyd_, Nov 23 2020
%Y Cf. A038094, A038096, A038097.
%K nonn,easy
%O 3,1
%A _Christian G. Bower_, Jan 04 1999; suggested by Vlady Ravelomanana
%E Terms a(12) and beyond corrected by _Andrew Howroyd_, Nov 23 2020
