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A229247 Number of set partitions of {1,...,n} with largest set of size 5. 2
1, 6, 42, 280, 1890, 12978, 91938, 671616, 5064345, 39439400, 317158842, 2631497232, 22512271964, 198412838820, 1800062132940, 16795556650200, 161038724157045, 1585408383273330, 16013462706719170, 165819496710741720, 1759058150311036806, 19103856738729254206 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 2 05:01 EST 2021. Contains 349437 sequences. (Running on oeis4.)