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 A038096 #22 Nov 23 2020 21:02:15
%S A038096 32,1280,61440,4587520,587202560,135291469824,57724360458240,
%T A038096 46443371157258240,71337018097548656640,211030752203237270487040,
%U A038096 1210134745434243803880882176,13518305228996352601898436526080
%N A038096 Number of rooted graphs on n labeled nodes where the root has degree 3.
%C A038096 The graphs are not necessarily connected. The nodes are labeled.
%H A038096 Andrew Howroyd, <a href="/A038096/b038096.txt">Table of n, a(n) for n = 4..50</a>
%F A038096 a(n) = n*binomial(n-1,3)*2^binomial(n-1,2). (There are n choices for the root, binomial(n-1,3) choices for the nodes it joined to, and 2^binomial(n-1,2) choices for the edges between the non-root nodes.)
%e A038096 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.
%t A038096 Table[n Binomial[n-1,3] 2^Binomial[n-1,2],{n,4,20}] (* _Harvey P. Dale_, Sep 14 2011 *)
%o A038096 (PARI) a(n) = {n*binomial(n-1,3)*2^binomial(n-1,2)} \\ _Andrew Howroyd_, Nov 23 2020
%Y A038096 Cf. A006125, A038094, A038095, A038097.
%K A038096 nonn,easy
%O A038096 4,1
%A A038096 _Christian G. Bower_, Jan 04 1999
%E A038096 Edited by _N. J. A. Sloane_, Sep 14 2011