A229245 Number of set partitions of {1,...,n} with largest set of size 3.

1, 4, 20, 90, 420, 2016, 10024, 51640, 276980, 1540440, 8899176, 53313624, 330835960, 2124646720, 14102514560, 96622736256, 682608577104, 4966188238080, 37166169295360, 285813960789280, 2256147419689856, 18263257380872064, 151466260791609600

Offset: 3

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 3..500

Crossrefs

Column k=3 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,3)-G(n,2):
seq(a(n), n=3..30);

Mathematica

b[n_, i_] := b[n, i] = If[n==0, 1, If[i<1, 0, Sum[b[n - i j, i - 1] n!/ i!^j/(n - i j)!/j!, {j, 0, n/i}]]];
a[n_] := b[n, 3] - b[n, 2];
a /@ Range[3, 30] (* Jean-François Alcover, Dec 10 2020, after Alois P. Heinz in A080510 *)

Formula

E.g.f.: exp(Sum_{j=1..3} x^j/j!) - exp(Sum_{j=1..2} x^j/j!).