A272522 Number of set partitions of [n] into ten blocks with distinct sizes.

1906765806522767212441719098019963758016000000, 9707171378661360354248751771737997313536000000, 101439940907011215701899456014662071926451200000, 829726696136835328433485294068646178065075200000, 7898017947032824439221398664897536276307929600000

Offset: 55

Author

Alois P. Heinz, May 01 2016

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 55..1000

Crossrefs

Column k=10 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, 10):
seq(a(n), n=55..65);

Formula

a(n) = n! * [x^n*y^10] Product_{n>=1} (1+y*x^n/n!).