A229248 Number of set partitions of {1,...,n} with largest set of size 6.

1, 7, 56, 420, 3150, 24024, 187110, 1497210, 12321309, 104379275, 910501592, 8176340536, 75557540604, 718108992888, 7015008076980, 70388350377492, 724955013327237, 7658820319677219, 82939240748756392, 920067296840668900, 10448713239329294930

Offset: 6

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 6..500

Crossrefs

Column k=6 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,6)-G(n,5):
seq(a(n), n=6..30);

Formula

E.g.f.: exp(Sum_{j=1..6} x^j/j!) - exp(Sum_{j=1..5} x^j/j!).