A099127 - OEIS

%I #12 Jan 17 2020 21:41:25

%S 1,9,1035,762355,2531986380,29653914688398,1023687680214527328,

%T 90954904732217610881940,18709083803797153776767847375,

%U 8183604949527627465377060678018870,7099997495119970047949715137555520213198

%N 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}.

%C 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.

%C a(n) is the number of n element multisets of n element multisets of a 9-set. - _Andrew Howroyd_, Jan 17 2020

%H Andrew Howroyd, <a href="/A099127/b099127.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = binomial(binomial(n + 8, n) + n - 1, n). - _Andrew Howroyd_, Jan 17 2020

%o (PARI) a(n)={binomial(binomial(n + 8, n) + n - 1, n)} \\ _Andrew Howroyd_, Jan 17 2020

%Y Column k=9 of A331436.

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

%K nonn

%O 0,2

%A _Sascha Kurz_, Oct 11 2004

%E a(0)=1 prepended and a(10) and beyond from _Andrew Howroyd_, Jan 17 2020