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A229246 Number of set partitions of {1,...,n} with largest set of size 4. 2
1, 5, 30, 175, 1015, 6111, 38010, 244035, 1624425, 11187605, 79695616, 586787565, 4460703065, 34979737625, 282686608170, 2352035472141, 20130594430095, 177076978131795, 1599554765785900, 14826174374092235, 140904888153964011, 1372081103132069275 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,2

LINKS

Alois P. Heinz, Table of n, a(n) for n = 4..500

FORMULA

E.g.f.: exp(Sum_{j=1..4} x^j/j!) - exp(Sum_{j=1..3} 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, 4)-G(n, 3):

seq(a(n), n=4..30);

MATHEMATICA

nn=25; Drop[Range[0, nn]!CoefficientList[Series[(Exp[x^4/4!]-1)Exp[x+x^2/2!+x^3/3!], {x, 0, nn}], x], 4] (* Geoffrey Critzer, Oct 09 2013 *)

CROSSREFS

Column k=4 of A080510.

Sequence in context: A084158 A111469 A241588 * A276598 A057088 A156195

Adjacent sequences:  A229243 A229244 A229245 * A229247 A229248 A229249

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Sep 17 2013

STATUS

approved

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Last modified February 21 04:18 EST 2019. Contains 320371 sequences. (Running on oeis4.)