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A268219 a(n) = (n!/4!)*Sum(1/k!,k=1..n-4).

%I A268219 #8 Jan 30 2016 16:56:56
%S A268219 0,0,0,0,0,5,45,350,2870,25956,259770,2857800,34294095,445823950,
%T A268219 6241536301,93623045880,1497968735900,25465468512680,458378433231300,
%U A268219 8709190231398576,174183804627976365,3657859897187509650,80472917738125219615,1850877107976880060000,44421050591445121450626
%N A268219 a(n) = (n!/4!)*Sum(1/k!,k=1..n-4).
%H A268219 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 A268219 g:=(r,n)->(n!/r!)*add(1/k!,k=1..n-r);
%p A268219 g2:=r->[seq(g(r,n),n=0..30)];
%p A268219 g2(4);
%o A268219 (PARI) a(n) = (n!/4!)*sum(k=1, n-4, 1/k!); \\ _Michel Marcus_, Jan 30 2016
%Y A268219 For others in this series, see A038156, A038158, A268218, A268220.
%K A268219 nonn
%O A268219 0,6
%A A268219 _N. J. A. Sloane_, Jan 30 2016