cp's OEIS Frontend

A272520 Number of set partitions of [n] into eight blocks with distinct sizes.

%I A272520 #4 May 01 2016 19:57:45
%S A272520 73566121315513295589120000,302438498741554659644160000,
%T A272520 2585849164240292339957568000,17681163441201479441398176000,
%U A272520 144230432460463828639480320000,1126747392322972404668523840000,11096383744399962905356299840000,126335461333640259667975104096000
%N A272520 Number of set partitions of [n] into eight blocks with distinct sizes.
%H A272520 Alois P. Heinz, <a href="/A272520/b272520.txt">Table of n, a(n) for n = 36..1000</a>
%F A272520 a(n) = n! * [x^n*y^8] Product_{n>=1} (1+y*x^n/n!).
%p A272520 b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
%p A272520       or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n,i-1,t)+
%p A272520       `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n,i))))
%p A272520     end:
%p A272520 a:= n-> b(n$2, 8):
%p A272520 seq(a(n), n=36..45);
%Y A272520 Column k=8 of A131632.
%K A272520 nonn
%O A272520 36,1
%A A272520 _Alois P. Heinz_, May 01 2016