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

65191584694745586153436251091200000, 299881289595829696305806755019520000, 2847357699192726409368266158771200000, 21355182743945448070261996190784000000, 188337379875526275760583438815706112000, 1546608042571126104473205339509472000000

Offset

45,1

Links

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

Formula

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

Maple

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

Crossrefs

Column k=9 of A131632.

Sequence in context: A095462 A115543 A219323 * A361899 A095464 A255360

Adjacent sequences: A272518 A272519 A272520 * A272522 A272523 A272524

Keyword

nonn

Author

Alois P. Heinz, May 01 2016

Status

approved