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

5,2

Links

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

Formula

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

Crossrefs

Column k=5 of A080510.

Sequence in context: A331706 A074429 A062310 * A105482 A242158 A157335

Adjacent sequences: A229244 A229245 A229246 * A229248 A229249 A229250

Keyword

nonn

Author

Alois P. Heinz, Sep 17 2013

Status

approved