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A097170
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Total number of minimal vertex covers among labeled trees on n nodes.
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6
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1, 2, 3, 40, 185, 3936, 35917, 978160, 14301513, 464105440, 9648558161, 361181788584, 9884595572293, 419174374377136, 14317833123918885, 679698565575210976, 27884513269105178033, 1468696946887669701312
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| S. Coulomb and M. Bauer, On vertex covers, matchings and random trees
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FORMULA
| Coulomb and Bauer give a g.f.
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MAPLE
| 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
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CROSSREFS
| Cf. A097171, A097172, A097173, A097174, A000169, A000272.
Sequence in context: A080393 A111683 A088984 * A176366 A157132 A077336
Adjacent sequences: A097167 A097168 A097169 * A097171 A097172 A097173
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KEYWORD
| nonn
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AUTHOR
| Ralf Stephan, Jul 30 2004
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EXTENSIONS
| More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2006
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