Search: id:A097170
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%I A097170
%S A097170 1,2,3,40,185,3936,35917,978160,14301513,464105440,9648558161,
%T A097170 361181788584,9884595572293,419174374377136,14317833123918885,
%U A097170 679698565575210976,27884513269105178033,1468696946887669701312
%N A097170 Total number of minimal vertex covers among labeled trees on n nodes.
%H A097170 S. Coulomb and M. Bauer, <a href="http://arXiv.org/abs/math.CO/0407456">
               On vertex covers, matchings and random trees</a>
%F A097170 Coulomb and Bauer give a g.f.
%p A097170 umax := 20 : u := array(0..umax) : T := proc(z) local resul,n ; global 
               umax,u ; resul :=0 ; for n from 1 to umax do resul := resul +n^(n-1)/
               n!*z^n ; od : RETURN(taylor(resul,x=0,umax+1)) ; end: U := proc() 
               global umax,u ; local resul,n ; resul :=0 ; for n from 0 to umax 
               do resul := resul+u[n]*x^n ; od: end: expU := proc() global umax,
               u ; taylor(exp(U()),x=0,umax+1) ; end: xUexpU := proc() global umax,
               u ; taylor(x*U()*expU(),x=0,umax+1) ; end: exexpU := proc() global 
               umax,u ; taylor(exp(x*expU())-1,x=0,umax+1) ; end: x2e2U := taylor((x*expU())^2,
               x=0,umax+1) ; A := expand(taylor(xUexpU()-T(x2e2U)*exexpU(), x=0,
               umax+1)) ; for n from 0 to umax do u[n] := solve(coeff(A,x,n+1),u[n]) 
               ; od ; F := proc() global umax,u ; taylor((1-U())*x*expU()-U()*T(x2e2U)+U()-U()^2/
               2,x=0,umax+1) ; end: egf := F() ; for n from 0 to umax-1 do n!*coeff(egf,
               x,n) ; od; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 
               2006
%Y A097170 Cf. A097171, A097172, A097173, A097174, A000169, A000272.
%Y A097170 Sequence in context: A080393 A111683 A088984 this_sequence A157132 A077336 
               A013646
%Y A097170 Adjacent sequences: A097167 A097168 A097169 this_sequence A097171 A097172 
               A097173
%K A097170 nonn
%O A097170 1,2
%A A097170 Ralf Stephan, Jul 30 2004
%E A097170 More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2006

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