A099128 Number of orbits of the wreath product of S_n with S_n on n X n matrices over {0,1,2,3,4,5,6,7,8,9}.

1, 10, 1540, 1798940, 10981240985, 269343686017406, 21897427636095471460, 5097399860176368033512080, 3028721298862926523085514684685, 4186904993091626163441378607213473000, 12477686558866630120430437118910496237274716

Offset

0,2

Comments

This is the number of possible votes of n referees judging n dancers by a mark between 0 and 9, where the referees cannot be distinguished.

a(n) is the number of n element multisets of n element multisets of a 10-set. - Andrew Howroyd, Jan 17 2020

Links

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

Formula

a(n) = binomial(binomial(n + 9, n) + n - 1, n). - Andrew Howroyd, Jan 17 2020

Prog

(PARI) a(n)={binomial(binomial(n + 9, n) + n - 1, n)} \\ Andrew Howroyd, Jan 17 2020

Crossrefs

Column k=10 of A331436.

Cf. A099121, A099122, A099123, A099124, A099125, A099126, A099127.

Sequence in context: A211914 A194792 A133216 * A172958 A286397 A160236

Adjacent sequences: A099125 A099126 A099127 * A099129 A099130 A099131

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