This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A038097 #15 Nov 23 2020 20:29:04
%S A038097 32,1120,53760,4155200,550305280,129990260736,56369709634560,
%T A038097 45808126727193600,70779622448719134720,210103333009795315650560,
%U A038097 1207180278201294640467288064,13500153139563947729371140096000,295095590701444457972767937903329280
%N A038097 Number of rooted connected graphs on n labeled nodes where the root has degree 3.
%H A038097 Andrew Howroyd, <a href="/A038097/b038097.txt">Table of n, a(n) for n = 4..50</a>
%F A038097 E.g.f.: B(x)/C(x) where B, C respectively are the e.g.f.'s for A038096 and A006125.
%e A038097 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.
%o A038097 (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
%Y A038097 Cf. A038094, A038095, A038096.
%K A038097 nonn,easy
%O A038097 4,1
%A A038097 _Christian G. Bower_, Jan 04 1999; suggested by Vlady Ravelomanana
%E A038097 Terms a(13) and beyond corrected by _Andrew Howroyd_, Nov 23 2020