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A058562
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Another 3-way generalization of series-parallel networks with n labeled edges.
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2
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0, 1, 3, 21, 243, 3933, 81819, 2080053, 62490339, 2166106509, 85092601707, 3735939709989, 181287330220467, 9634718677393917, 556569415611455931, 34723276781195740437, 2326773811332029313411, 166666995789875216053101
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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FORMULA
| E.g.f.: -3/2*LambertW(-2/3*exp(-2/3+1/3*x))-1. - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 25 2007
E.g.f.: A(x) = Series_Reversion[ 3*log(1+x) - 2*x ]. [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 03 2008]
Let f(x) = (1+x)/(1-2*x). Let D be the operator g(x) -> d/dx(f(x)*g(x)). Then for n>=1, a(n) = D^(n-1)(1) evaluated at x = 0. - Peter Bala, Sep 05 2011
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MAPLE
| spec := [ N, {N=Union(Z, S, P, Q), S=Set(Union(Z, P, Q), card>=2), P=Set(Union(Z, S, Q), card>=2), Q=Set(Union(Z, S, P), card>=2)}, labeled ]; [seq(combstruct[count](spec, size=n), n=0..40)]; # N=A058562, S=A058575
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PROG
| (PARI) {a(n)=if(n<1, 0, n!*polcoeff(serreverse(3*log(1+x+x*O(x^n))-2*x), n))} [From Paul D. Hanna (pauldhanna(AT)juno.com), Aug 03 2008]
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CROSSREFS
| Cf. A058540, A058371, A058575.
Sequence in context: A078586 A179331 A138903 * A145083 A138213 A193333
Adjacent sequences: A058559 A058560 A058561 * A058563 A058564 A058565
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), Dec 26 2000
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