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A268218 a(n) = (n!/3!)*Sum(1/k!,k=1..n-3).

%I A268218 #8 Jan 30 2016 16:56:45
%S A268218 0,0,0,0,4,30,200,1435,11536,103908,1039200,11431365,137176600,
%T A268218 1783296086,24966145568,374492183975,5991874944160,101861874051400,
%U A268218 1833513732926016,34836760925595273,696735218511906600,14631439588750039930,321891670952500880000,7403508431907520241771
%N A268218 a(n) = (n!/3!)*Sum(1/k!,k=1..n-3).
%H A268218 G. A. Kamel, <a href="http://www.aascit.org/journal/archive2?journalId=928&amp;paperId=2310">Partial Chain Topologies on Finite Sets</a>, Computational and Applied Mathematics Journal. Vol. 1, No. 4, 2015, pp. 174-179.
%p A268218 g:=(r,n)->(n!/r!)*add(1/k!,k=1..n-r);
%p A268218 g2:=r->[seq(g(r,n),n=0..30)];
%p A268218 g2(3);
%o A268218 (PARI) a(n) = (n!/3!)*sum(k=1, n-3, 1/k!); \\ _Michel Marcus_, Jan 30 2016
%Y A268218 For others in this series, see A038156, A038158, A268219, A268220.
%K A268218 nonn
%O A268218 0,5
%A A268218 _N. J. A. Sloane_, Jan 30 2016