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

73566121315513295589120000, 302438498741554659644160000, 2585849164240292339957568000, 17681163441201479441398176000, 144230432460463828639480320000, 1126747392322972404668523840000, 11096383744399962905356299840000, 126335461333640259667975104096000

Offset: 36

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 36..1000

Crossrefs

Column k=8 of A131632.

Programs

Maple

b:= proc(n, i, t) option remember; `if`(t>i or t*(t+1)/2>n
      or t*(2*i+1-t)/2n, 0, b(n-i, i-1, t-1)*binomial(n,i))))
    end:
a:= n-> b(n$2, 8):
seq(a(n), n=36..45);

Formula

a(n) = n! * [x^n*y^8] Product_{n>=1} (1+y*x^n/n!).