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 A218378 Number of simple labeled graphs on n nodes with all odd size components. 1

%I #10 Oct 30 2012 16:53:43

%S 1,1,1,5,17,769,4609,1882805,15138593,66365067361,664157177281,

%T 35645315131333445,427773958289546417,301274983519644591252769,

%U 4217875813061550908307649,40527712572140444650575170520245,648443738687003872454538321727553

%N Number of simple labeled graphs on n nodes with all odd size components.

%F E.g.f.: exp( (A(x) - A(-x))/2 ) where A(x) is the e.g.f. for A001187.

%t nn=21; a=Sum[2^Binomial[n,2]x^n/n!,{n,0,nn}]; c=Range[0,nn]! CoefficientList[Series[ Log[a]+1, {x,0,nn}], x]; cox= Sum[c[[i]]x^(i-1)/(i-1)!, {i,2,nn,2}]; Select[Range[0,nn]! CoefficientList[Series[Exp[cox],{x,0,nn}], x], #>0&]

%Y Cf. A218377, A182124.

%K nonn

%O 0,4

%A _Geoffrey Critzer_, Oct 27 2012

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