A229247 Number of set partitions of {1,...,n} with largest set of size 5.

1, 6, 42, 280, 1890, 12978, 91938, 671616, 5064345, 39439400, 317158842, 2631497232, 22512271964, 198412838820, 1800062132940, 16795556650200, 161038724157045, 1585408383273330, 16013462706719170, 165819496710741720, 1759058150311036806, 19103856738729254206

Offset: 5

Author

Alois P. Heinz, Sep 17 2013

Keywords

• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..500

Crossrefs

Column k=5 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,5)-G(n,4):
seq(a(n), n=5..30);

Mathematica

nmin = size = 5; nmax = 30;
g[k_] := Exp[Sum[x^j/j!, {j, 1, k}]];
cc = CoefficientList[g[size]-g[size-1]+O[x]^(nmax+1), x]*Range[0, nmax]!;
a[n_] := cc[[n+1]];
a /@ Range[nmin, nmax] (* Jean-François Alcover, Mar 07 2021 *)

Formula

E.g.f.: exp(Sum_{j=1..5} x^j/j!) - exp(Sum_{j=1..4} x^j/j!).