A099127 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4,5,6,7,8}.

1, 9, 1035, 762355, 2531986380, 29653914688398, 1023687680214527328, 90954904732217610881940, 18709083803797153776767847375, 8183604949527627465377060678018870, 7099997495119970047949715137555520213198

Offset

0,2

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 8, where the referees cannot be distinguished.

a(n) is the number of n element multisets of n element multisets of a 9-set. - Andrew Howroyd, Jan 17 2020

Links

Andrew Howroyd, Table of n, a(n) for n = 0..50

Formula

a(n) = binomial(binomial(n + 8, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Prog

(PARI) a(n)={binomial(binomial(n + 8, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Crossrefs

Column k=9 of A331436.

Cf. A099121, A099122, A099123, A099124, A099125, A099126, A099128.

Sequence in context: A197781 A197612 A004809 * A172944 A277829 A286396

Adjacent sequences: A099124 A099125 A099126 * A099128 A099129 A099130

Keyword

nonn

Author

Sascha Kurz, Oct 11 2004

Extensions

a(0)=1 prepended and a(10) and beyond from Andrew Howroyd, Jan 17 2020

Status

approved