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

%I A229247 #9 Mar 07 2021 04:23:15
%S A229247 1,6,42,280,1890,12978,91938,671616,5064345,39439400,317158842,
%T A229247 2631497232,22512271964,198412838820,1800062132940,16795556650200,
%U A229247 161038724157045,1585408383273330,16013462706719170,165819496710741720,1759058150311036806,19103856738729254206
%N A229247 Number of set partitions of {1,...,n} with largest set of size 5.
%H A229247 Alois P. Heinz, <a href="/A229247/b229247.txt">Table of n, a(n) for n = 5..500</a>
%F A229247 E.g.f.: exp(Sum_{j=1..5} x^j/j!) - exp(Sum_{j=1..4} x^j/j!).
%p A229247 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229247       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229247       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229247     end:
%p A229247 a:= n-> G(n,5)-G(n,4):
%p A229247 seq(a(n), n=5..30);
%t A229247 nmin = size = 5; nmax = 30;
%t A229247 g[k_] := Exp[Sum[x^j/j!, {j, 1, k}]];
%t A229247 cc = CoefficientList[g[size]-g[size-1]+O[x]^(nmax+1), x]*Range[0, nmax]!;
%t A229247 a[n_] := cc[[n+1]];
%t A229247 a /@ Range[nmin, nmax] (* _Jean-François Alcover_, Mar 07 2021 *)
%Y A229247 Column k=5 of A080510.
%K A229247 nonn
%O A229247 5,2
%A A229247 _Alois P. Heinz_, Sep 17 2013