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

65191584694745586153436251091200000, 299881289595829696305806755019520000, 2847357699192726409368266158771200000, 21355182743945448070261996190784000000, 188337379875526275760583438815706112000, 1546608042571126104473205339509472000000

Offset: 45

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 45..1000

Crossrefs

Column k=9 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, 9):
seq(a(n), n=45..55);

Formula

a(n) = n! * [x^n*y^9] Product_{n>=1} (1+y*x^n/n!).