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

7,2

Links

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

Formula

E.g.f.: exp(Sum_{j=1..7} x^j/j!) - exp(Sum_{j=1..6} 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, 7)-G(n, 6):
seq(a(n), n=7..30);

Crossrefs

Column k=7 of A080510.

Sequence in context: A052379 A246940 A158798 * A242160 A343365 A062541

Adjacent sequences: A229246 A229247 A229248 * A229250 A229251 A229252

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2013

Status

approved