A229251 Number of set partitions of {1,...,n} with largest set of size 9.

1, 10, 110, 1100, 10725, 104104, 1016015, 10032880, 100643400, 1028142830, 10712984282, 113961363880, 1238298284860, 13747432565790, 155944562191220, 1807325391776872, 21396572780305250, 258695925902828700, 3193365395052825850, 40233167990427412000

Offset: 9

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 9..500

Crossrefs

Column k=9 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,9)-G(n,8):
seq(a(n), n=9..30);

Formula

E.g.f.: exp(Sum_{j=1..9} x^j/j!) - exp(Sum_{j=1..8} x^j/j!).