A229252 Number of set partitions of {1,...,n} with largest set of size 10.

1, 11, 132, 1430, 15015, 156156, 1625624, 17055896, 181158120, 1953517566, 21426984722, 239340203466, 2724654560628, 31626047962432, 374383760685660, 4520229252281160, 55662052670665870, 698975472340315170, 8949358054013356980, 116803043793523277190

Offset: 10

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 10..500

Crossrefs

Column k=10 of A080510.

Programs

Maple

G:= proc(n, k) option remember; local j; if k>n then G(n, n)
      elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
      for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
    end:
a:= n-> G(n,10)-G(n,9):
seq(a(n), n=10..30);

Formula

E.g.f.: exp(Sum_{j=1..10} x^j/j!) - exp(Sum_{j=1..9} x^j/j!).