A099122 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3}.

1, 4, 55, 1540, 73815, 5461512, 581106988, 84431259000, 16104878212995, 3910294246315600, 1178924607035010836, 432472873725488656424, 189789513537655207705620, 98222259182333060014344720

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 3, where the referees cannot be distinguished.

a(n) is the number n element multisets of n element multisets of a 4-set. - Andrew Howroyd, Jan 17 2020

Links

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

Crossrefs

Column k=4 of A331436.

Cf. A099121, A099123, A099124, A099125, A099126, A099127, A099128.

Programs

PARI

a(n)={binomial(binomial(n+3, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Formula

a(n) = binomial(binomial(n+3, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Extensions

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