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Search: id:A097171
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| A097171 |
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Number of maximal matchings among labeled trees on n nodes. |
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+0
5
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| 1, 1, 6, 24, 320, 3270, 55482, 999656, 21718440, 544829130, 15130478990, 475440344412, 16294653237876, 613546243029902, 25016884214147490, 1100408748640263120, 51948228453097163312, 2617775548597611727506
(list; graph; listen)
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OFFSET
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1,3
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LINKS
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S. Coulomb and M. Bauer, On vertex covers, matchings, and random trees
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FORMULA
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Coulomb and Bauer give a g.f.
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MAPLE
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umax := 20 ; u := array(0..umax) ; 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: xexpU := proc() global umax, u ; taylor(x*expU(), x=0, umax+1) ; end: exexpU := proc() global umax, u ; local t ; t := xexpU() ; taylor(exp(-t^2+t+3*U()), x=0, umax+1) ; end: A := expand(taylor(U()-x^2*exexpU(), x=0, umax+1)) ; for n from 0 to umax do u[n] := solve(coeff(A, x, n), u[n]) ; od : F := proc() t := xexpU() ; taylor(-(t+U())^2/2+(1+U()*t)*t+U()-U()^2, x=0, umax+1) ; end: egf := F() ; for n from 1 to umax do n!*coeff(egf, x, n) ; od; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2006
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CROSSREFS
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Cf. A097170, A097172, A097173, A097174, A000169, A000272.
Sequence in context: A052671 A052733 A010567 this_sequence A128614 A139240 A052524
Adjacent sequences: A097168 A097169 A097170 this_sequence A097172 A097173 A097174
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan, Jul 30 2004
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Sep 14 2006
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