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A108528
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Number of increasing mobiles (cycle rooted trees) with n generators.
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2
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1, 2, 10, 92, 1216, 20792, 435520, 10793792, 308874016, 10021509632, 363509706880, 14576530558592, 640275236943616, 30573223563625472, 1576805482203235840, 87353392124392020992, 5173324070004374358016, 326160898887563325581312, 21810458629345555407462400
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OFFSET
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1,2
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COMMENTS
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In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
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LINKS
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FORMULA
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E.g.f. satisfies 2*A(x) = x - 1 + A'(x) - log(1-A(x)).
E.g.f. satisfies: (1+A(x))*sqrt(1-A(x)^2) = exp(x).
E.g.f.: A(x) = Series_Reversion[ log((1+x)*sqrt(1-x^2)) ]. (End)
a(n) ~ 2^(n-2) * sqrt(3) * n^(n-1) / (exp(n) * (log(27/16))^(n-1/2)). - Vaclav Kotesovec, Jan 08 2014
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MATHEMATICA
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Rest[CoefficientList[InverseSeries[Series[Log[(1+x)*Sqrt[1-x^2]], {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 08 2014 *)
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PROG
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(PARI) {a(n)=n!*polcoeff(serreverse(log((1+x)*sqrt(1-x^2+O(x^(n+2))))), n)} \\ Paul D. Hanna, Sep 11 2010
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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