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 A198861 #18 Aug 25 2014 04:43:34
%S A198861 2,30,1680,7983360,40548366802944000
%N A198861 The number of ways to paint the faces of the five Platonic solids using exactly n colors where n is the number of faces of each solid.
%C A198861 Let G, the group of rotations in 3 dimensional space act on the set of n! paintings of each Platonic solid having n faces. There are n! fixed points in the action table since the only element in G that leaves a painting fixed is the identity element. The order of G is A098427/2. So by Burnside's Lemma a(n)=n!/|G|.
%H A198861 David Broughton's Puzzles & Programs, <a href="http://www.iwpcug.org/davidbro/puz0807.htm">Colouring The Platonic Solids</a>
%F A198861 a(n) = A053016(n)!/(2*A063722(n)) (see link). - _Michel Marcus_, Aug 24 2014
%o A198861 (PARI) lista() = {ve = [6, 12, 12, 30, 30 ]; vf = [4, 6, 8, 12, 20 ]; for (i=1, 5, nb = vf[i]!/(2*ve[i]); print1(nb, ", "););} \\ _Michel Marcus_, Aug 25 2014
%Y A198861 Cf. A053016 (number of faces), A063722 (number of edges).
%K A198861 nonn,fini,full
%O A198861 1,1
%A A198861 _Geoffrey Critzer_, Oct 30 2011