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

4,2

Links

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

Formula

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

Crossrefs

Column k=4 of A080510.

Sequence in context: A084158 A111469 A241588 * A276598 A057088 A156195

Adjacent sequences: A229243 A229244 A229245 * A229247 A229248 A229249

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2013

Status

approved