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%I #15 Jan 17 2020 23:02:00
%S 1,3,21,220,3060,53130,1107568,26978328,752538150,23667689815,
%T 828931106355,32006008361808,1350990969850340,61902409203193230,
%U 3060335715568296000,162392216278033616560,9206887338937200407418
%N Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2}.
%C This is the number of possible votes of n referees judging n dancers by a mark between 0 and 2, where the referees cannot be distinguished.
%C a(n) is the number of n element multisets of n element multisets of a 3-set. - _Andrew Howroyd_, Jan 17 2020
%H Andrew Howroyd, <a href="/A099121/b099121.txt">Table of n, a(n) for n = 0..100</a>
%F a(n) = binomial( (n+1)*(n+2)/2 + n-1, n).
%F a(n) = binomial(binomial(n + 2, n) + n - 1, n). - _Andrew Howroyd_, Jan 17 2020
%o (PARI) a(n)={binomial(binomial(n + 2, n) + n - 1, n)} \\ _Andrew Howroyd_, Jan 17 2020
%Y Column k=2 of A107862 and A331436.
%Y Cf. A099122, 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
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