A229246 Number of set partitions of {1,...,n} with largest set of size 4.

1, 5, 30, 175, 1015, 6111, 38010, 244035, 1624425, 11187605, 79695616, 586787565, 4460703065, 34979737625, 282686608170, 2352035472141, 20130594430095, 177076978131795, 1599554765785900, 14826174374092235, 140904888153964011, 1372081103132069275

Offset: 4

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..500

Crossrefs

Column k=4 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,4)-G(n,3):
seq(a(n), n=4..30);

Mathematica

nn=25;Drop[Range[0,nn]!CoefficientList[Series[(Exp[x^4/4!]-1)Exp[x+x^2/2!+x^3/3!],{x,0,nn}],x],4] (* Geoffrey Critzer, Oct 09 2013 *)

Formula

E.g.f.: exp(Sum_{j=1..4} x^j/j!) - exp(Sum_{j=1..3} x^j/j!).