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A229248 Number of set partitions of {1,...,n} with largest set of size 6.

%I A229248 #4 Sep 17 2013 19:03:41
%S A229248 1,7,56,420,3150,24024,187110,1497210,12321309,104379275,910501592,
%T A229248 8176340536,75557540604,718108992888,7015008076980,70388350377492,
%U A229248 724955013327237,7658820319677219,82939240748756392,920067296840668900,10448713239329294930
%N A229248 Number of set partitions of {1,...,n} with largest set of size 6.
%H A229248 Alois P. Heinz, <a href="/A229248/b229248.txt">Table of n, a(n) for n = 6..500</a>
%F A229248 E.g.f.: exp(Sum_{j=1..6} x^j/j!) - exp(Sum_{j=1..5} x^j/j!).
%p A229248 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229248       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229248       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229248     end:
%p A229248 a:= n-> G(n,6)-G(n,5):
%p A229248 seq(a(n), n=6..30);
%Y A229248 Column k=6 of A080510.
%K A229248 nonn
%O A229248 6,2
%A A229248 _Alois P. Heinz_, Sep 17 2013