A229250 Number of set partitions of {1,...,n} with largest set of size 8.

1, 9, 90, 825, 7425, 66924, 609609, 5643495, 53275365, 513949865, 5072383602, 51247279161, 530162317815, 5616049288500, 60907673202255, 676114396423257, 7679484722988045, 89216205660482175, 1059689275333095550, 12863300130089805825, 159506272335882076605

Offset: 8

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 8..500

Crossrefs

Column k=8 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,8)-G(n,7):
seq(a(n), n=8..30);

Formula

E.g.f.: exp(Sum_{j=1..8} x^j/j!) - exp(Sum_{j=1..7} x^j/j!).