A099123 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4}.

1, 5, 120, 7770, 1088430, 286243776, 127860662755, 90079147136880, 94572327271677750, 141504997346476482290, 291098519807782284023426, 799388312264077003441393875, 2859142263297618955891805452700

Offset

0,2

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 4, where the referees cannot be distinguished.

a(n) is the number of n element multisets of n element multisets of a 5-set. - Andrew Howroyd, Jan 17 2020

Links

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

Formula

a(n) = binomial(binomial(n + 4, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Prog

(PARI) a(n)={binomial(binomial(n + 4, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Crossrefs

Column k=5 of A331436.

Cf. A099121, A099122, A099124, A099125, A099126, A099127, A099128.

Sequence in context: A252928 A308363 A192639 * A097993 A172806 A054752

Adjacent sequences: A099120 A099121 A099122 * A099124 A099125 A099126

Keyword

nonn

Author

Sascha Kurz, Sep 28 2004

Extensions

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

Status

approved