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%I #17 Apr 18 2017 07:04:11
%S 0,0,2,3,16,65,456,3157,28624,276705,3136240,38531141,528468744,
%T 7837577761,126588882616,2194957583925,40854219413536,810192673705793,
%U 17082845929433952,381225135102420997
%N E.g.f.: log(-1/(-1+x*exp(x)-x)).
%C Previous name was: A simple grammar.
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=826">Encyclopedia of Combinatorial Structures 826</a>
%F E.g.f.: log(-1/(-1+x*exp(x)-x))
%F a(n) ~ (n-1)! * r^n, where r = 1.23997788765655... is the root of the equation log(1+r)=1/r. - _Vaclav Kotesovec_, Sep 29 2013
%F a(n) = n!*Sum_{k=1..n/2}((k-1)!*stirling2(n-k,k)/(n-k)!). - _Vladimir Kruchinin_, Mar 22 2016
%p spec := [S,{B=Set(Z,1 <= card),C=Prod(Z,B),S=Cycle(C)},labeled]: seq(combstruct[count](spec, size=n), n=0..20);
%t CoefficientList[Series[Log[-1/(-1+x*E^x-x)], {x, 0, 20}], x]* Range[0, 20]! (* _Vaclav Kotesovec_, Sep 29 2013 *)
%o (Maxima)
%o a(n):=(n)!*sum((k-1)!*stirling2(n-k,k)/(n-k)!,k,1,n/2); /* _Vladimir Kruchinin_, Mar 22 2016 */
%K easy,nonn
%O 0,3
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E New name using e.g.f. by _Joerg Arndt_, Sep 30 2013