editing

approved

Alois P. Heinz, <a href="/A272518/b272518.txt">Table of n, a(n) for n = 21..1000</a>

allocated for Alois P. Heinz

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

2053230379200, 6453009763200, 43288940494800, 242418066770880, 1707999012720000, 12887361202716000, 144924867388501200, 620550897351184800, 4048435123506774000, 23424084614648718000, 161250104584826056800, 1013722794731975328000, 8616255173755280251200

21,1

a(n) = n! * [x^n*y^6] Product_{n>=1} (1+y*x^n/n!).

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

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

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

end:

a:= n-> b(n$2, 6):

seq(a(n), n=21..40);

Column k=6 of A131632.

allocated

nonn

Alois P. Heinz, May 01 2016

approved

editing

allocated for Alois P. Heinz

allocated

approved