A272522 - OEIS

%I #4 May 01 2016 20:06:32

%S 1906765806522767212441719098019963758016000000,

%T 9707171378661360354248751771737997313536000000,

%U 101439940907011215701899456014662071926451200000,829726696136835328433485294068646178065075200000,7898017947032824439221398664897536276307929600000

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

%H Alois P. Heinz, <a href="/A272522/b272522.txt">Table of n, a(n) for n = 55..1000</a>

%F a(n) = n! * [x^n*y^10] 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, 10):

%p seq(a(n), n=55..65);

%Y Column k=10 of A131632.

%K nonn

%O 55,1

%A _Alois P. Heinz_, May 01 2016