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%I #18 Apr 18 2017 07:04:11
%S 1,2,4,14,76,542,4684,47294,545836,7087262,102247564,1622632574,
%T 28091567596,526858348382,10641342970444,230283190977854,
%U 5315654681981356,130370767029135902,3385534663256845324
%N E.g.f.: (1-3*exp(x)+exp(2*x))/(exp(x)-2).
%C Previous name was: A simple grammar.
%C Stirling transform of A005212(n-1)=[1,1,0,6,0,120,0,...] is a(n-1)=[1,2,4,14,76,...]. - _Michael Somos_, Mar 04 2004
%C Stirling transform of (-1)^n*A052612(n-1)=[0,2,-2,12,-24,...] is a(n-1)=[0,2,4,14,76,...]. - _Michael Somos_, Mar 04 2004
%C Stirling transform of A000142(n)=[2,2,6,24,120,...] is a(n)=[2,2,4,14,76,...]. - _Michael Somos_, Mar 04 2004
%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=824">Encyclopedia of Combinatorial Structures 824</a>
%F E.g.f.: (1-3*exp(x)+exp(x)^2)/(-2+exp(x))
%F a(n) ~ n!/(2*(log(2))^(n+1)). - _Vaclav Kotesovec_, Oct 05 2013
%p spec := [S,{B=Sequence(C),C=Set(Z,1 <= card),S=Union(B,C)},labeled]: seq(combstruct[count](spec,size=n), n=0..20);
%t With[{nn=20},CoefficientList[Series[(1-3Exp[x]+Exp[x]^2)/(-2+Exp[x]),{x,0,nn}],x]Range[0,nn]!] (* _Harvey P. Dale_, Nov 24 2012 *)
%o (PARI) a(n)=if(n<0,0,n!*polcoeff(subst(y+1/(1-y),y,exp(x+x*O(x^n))-1),n))
%Y A000670(n)=a(n)-1, if n>0. A032109(n)=a(n)/2, if n>0.
%Y A000629, A000670, A002050, A052856, A076726 are all more-or-less the same sequence. - _N. J. A. Sloane_, Jul 04 2012
%K easy,nonn
%O 0,2
%A encyclopedia(AT)pommard.inria.fr, Jan 25 2000
%E New name using e.g.f., _Vaclav Kotesovec_, Oct 05 2013
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