A229249 Number of set partitions of {1,...,n} with largest set of size 7.

1, 8, 72, 600, 4950, 41184, 348348, 3008148, 26608725, 241395440, 2247683152, 21485909952, 210840271980, 2123351405280, 21937875152760, 232419281905272, 2523691371079725, 28070949453307992, 319668800125675000, 3725037254807468600, 44393091629344788330

Offset: 7

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 7..500

Crossrefs

Column k=7 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,7)-G(n,6):
seq(a(n), n=7..30);

Formula

E.g.f.: exp(Sum_{j=1..7} x^j/j!) - exp(Sum_{j=1..6} x^j/j!).