A229246 - OEIS

%I #7 Oct 09 2013 19:54:40

%S 1,5,30,175,1015,6111,38010,244035,1624425,11187605,79695616,

%T 586787565,4460703065,34979737625,282686608170,2352035472141,

%U 20130594430095,177076978131795,1599554765785900,14826174374092235,140904888153964011,1372081103132069275

%N Number of set partitions of {1,...,n} with largest set of size 4.

%H Alois P. Heinz, <a href="/A229246/b229246.txt">Table of n, a(n) for n = 4..500</a>

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

%p G:= proc(n, k) option remember; local j; if k>n then G(n, n)

%p       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);

%p       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi

%p     end:

%p a:= n-> G(n,4)-G(n,3):

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

%t 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 *)

%Y Column k=4 of A080510.

%K nonn

%O 4,2

%A _Alois P. Heinz_, Sep 17 2013