%I #10 Jan 17 2020 20:23:11
%S 1,4,55,1540,73815,5461512,581106988,84431259000,16104878212995,
%T 3910294246315600,1178924607035010836,432472873725488656424,
%U 189789513537655207705620,98222259182333060014344720
%N Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3}.
%C This is the number of possible votes of n referees judging n dancers by a mark between 0 and 3, where the referees cannot be distinguished.
%C a(n) is the number n element multisets of n element multisets of a 4-set. - _Andrew Howroyd_, Jan 17 2020
%H Andrew Howroyd, <a href="/A099122/b099122.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = binomial(binomial(n+3, n) + n - 1, n). - _Andrew Howroyd_, Jan 17 2020
%o (PARI) a(n)={binomial(binomial(n+3, n) + n - 1, n)} \\ _Andrew Howroyd_, Jan 17 2020
%Y Column k=4 of A331436.
%Y Cf. A099121, A099123, A099124, A099125, A099126, A099127, A099128.
%K nonn
%O 0,2
%A _Sascha Kurz_, Sep 28 2004
%E a(0)=1 prepended by _Andrew Howroyd_, Jan 17 2020