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

3,2

Links

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

Formula

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

Crossrefs

Column k=3 of A080510.

Sequence in context: A017965 A180284 A065180 * A328153 A070733 A166175

Adjacent sequences: A229242 A229243 A229244 * A229246 A229247 A229248

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2013

Status

approved