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A038095 Number of rooted connected graphs on n labeled nodes where the root has degree 2. 4

%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(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

%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

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Last modified January 22 14:15 EST 2021. Contains 340362 sequences. (Running on oeis4.)