cp's OEIS Frontend

A272521 Number of set partitions of [n] into nine blocks with distinct sizes.

%I A272521 #4 May 01 2016 20:02:35
%S A272521 65191584694745586153436251091200000,
%T A272521 299881289595829696305806755019520000,
%U A272521 2847357699192726409368266158771200000,21355182743945448070261996190784000000,188337379875526275760583438815706112000,1546608042571126104473205339509472000000
%N A272521 Number of set partitions of [n] into nine blocks with distinct sizes.
%H A272521 Alois P. Heinz, <a href="/A272521/b272521.txt">Table of n, a(n) for n = 45..1000</a>
%F A272521 a(n) = n! * [x^n*y^9] Product_{n>=1} (1+y*x^n/n!).
%p A272521 b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
%p A272521       or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n,i-1,t)+
%p A272521       `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n,i))))
%p A272521     end:
%p A272521 a:= n-> b(n$2, 9):
%p A272521 seq(a(n), n=45..55);
%Y A272521 Column k=9 of A131632.
%K A272521 nonn
%O A272521 45,1
%A A272521 _Alois P. Heinz_, May 01 2016