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A268220 a(n) = (n!/5!)*Sum(1/k!,k=1..n-5).

%I A268220 #8 Jan 30 2016 16:57:07
%S A268220 0,0,0,0,0,0,6,63,560,5166,51912,571494,6858720,89164647,1248307060,
%T A268220 18724608903,299593746816,5093093702060,91675686645648,
%U A268220 1741838046278940,34836760925594304,731571979437500733,16094583547625042460,370175421595376010229,8884210118289024288000
%N A268220 a(n) = (n!/5!)*Sum(1/k!,k=1..n-5).
%H A268220 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 A268220 g:=(r,n)->(n!/r!)*add(1/k!,k=1..n-r);
%p A268220 g2:=r->[seq(g(r,n),n=0..30)];
%p A268220 g2(5);
%o A268220 (PARI) a(n) = (n!/5!)*sum(k=1, n-5, 1/k!); \\ _Michel Marcus_, Jan 30 2016
%Y A268220 For others in this series, see A038156, A038158, A268218, A268219.
%K A268220 nonn
%O A268220 0,7
%A A268220 _N. J. A. Sloane_, Jan 30 2016