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A272518 Number of set partitions of [n] into six blocks with distinct sizes.

%I A272518 #4 May 01 2016 19:49:35
%S A272518 2053230379200,6453009763200,43288940494800,242418066770880,
%T A272518 1707999012720000,12887361202716000,144924867388501200,
%U A272518 620550897351184800,4048435123506774000,23424084614648718000,161250104584826056800,1013722794731975328000,8616255173755280251200
%N A272518 Number of set partitions of [n] into six blocks with distinct sizes.
%H A272518 Alois P. Heinz, <a href="/A272518/b272518.txt">Table of n, a(n) for n = 21..1000</a>
%F A272518 a(n) = n! * [x^n*y^6] Product_{n>=1} (1+y*x^n/n!).
%p A272518 b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
%p A272518       or t*(2*i+1-t)/2<n, 0, `if`(n=0, 1, b(n,i-1,t)+
%p A272518       `if`(i>n, 0, b(n-i, i-1, t-1)*binomial(n,i))))
%p A272518     end:
%p A272518 a:= n-> b(n$2, 6):
%p A272518 seq(a(n), n=21..40);
%Y A272518 Column k=6 of A131632.
%K A272518 nonn
%O A272518 21,1
%A A272518 _Alois P. Heinz_, May 01 2016