%I #4 May 01 2016 20:02:35

%S 65191584694745586153436251091200000,

%T 299881289595829696305806755019520000,

%U 2847357699192726409368266158771200000,21355182743945448070261996190784000000,188337379875526275760583438815706112000,1546608042571126104473205339509472000000

%N Number of set partitions of [n] into nine blocks with distinct sizes.

%H Alois P. Heinz, <a href="/A272521/b272521.txt">Table of n, a(n) for n = 45..1000</a>

%F a(n) = n! * [x^n*y^9] Product_{n>=1} (1+y*x^n/n!).

%p b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n

%p or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n,i-1,t)+

%p `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n,i))))

%p end:

%p a:= n-> b(n$2, 9):

%p seq(a(n), n=45..55);

%Y Column k=9 of A131632.

%K nonn

%O 45,1

%A _Alois P. Heinz_, May 01 2016