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A229249 Number of set partitions of {1,...,n} with largest set of size 7.

%I A229249 #4 Sep 17 2013 19:14:05
%S A229249 1,8,72,600,4950,41184,348348,3008148,26608725,241395440,2247683152,
%T A229249 21485909952,210840271980,2123351405280,21937875152760,
%U A229249 232419281905272,2523691371079725,28070949453307992,319668800125675000,3725037254807468600,44393091629344788330
%N A229249 Number of set partitions of {1,...,n} with largest set of size 7.
%H A229249 Alois P. Heinz, <a href="/A229249/b229249.txt">Table of n, a(n) for n = 7..500</a>
%F A229249 E.g.f.: exp(Sum_{j=1..7} x^j/j!) - exp(Sum_{j=1..6} x^j/j!).
%p A229249 G:= proc(n, k) option remember; local j; if k>n then G(n, n)
%p A229249       elif n=0 then 1 elif k<1 then 0 else G(n-k, k);
%p A229249       for j from k-1 to 1 by -1 do %*(n-j)/j +G(n-j, k) od; % fi
%p A229249     end:
%p A229249 a:= n-> G(n,7)-G(n,6):
%p A229249 seq(a(n), n=7..30);
%Y A229249 Column k=7 of A080510.
%K A229249 nonn
%O A229249 7,2
%A A229249 _Alois P. Heinz_, Sep 17 2013