A099121 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2}.

1, 3, 21, 220, 3060, 53130, 1107568, 26978328, 752538150, 23667689815, 828931106355, 32006008361808, 1350990969850340, 61902409203193230, 3060335715568296000, 162392216278033616560, 9206887338937200407418

Offset: 0

Author

Sascha Kurz, Sep 28 2004

Keywords

• nonn

Comments

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.

a(n) is the number of n element multisets of n element multisets of a 3-set. - Andrew Howroyd, Jan 17 2020

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..100

Crossrefs

Column k=2 of A107862 and A331436.

Cf. A099122, A099123, A099124, A099125, A099126, A099127, A099128.

Programs

PARI

a(n)={binomial(binomial(n + 2, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial( (n+1)*(n+2)/2 + n-1, n).

a(n) = binomial(binomial(n + 2, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

a(0)=1 prepended by Andrew Howroyd, Jan 17 2020