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

9,2

Links

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

Formula

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

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);

Crossrefs

Column k=9 of A080510.

Sequence in context: A289767 A290207 A286620 * A290672 A290417 A289405

Adjacent sequences: A229248 A229249 A229250 * A229252 A229253 A229254

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2013

Status

approved