A108528 Number of increasing mobiles (cycle rooted trees) with n generators.

1, 2, 10, 92, 1216, 20792, 435520, 10793792, 308874016, 10021509632, 363509706880, 14576530558592, 640275236943616, 30573223563625472, 1576805482203235840, 87353392124392020992, 5173324070004374358016, 326160898887563325581312, 21810458629345555407462400

Offset: 1

Author

Christian G. Bower, Jun 07 2005

Keywords

• nonn

Comments

In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..200
• Index entries for sequences related to mobiles

Crossrefs

Cf. A108521, A108522, A108523, A108524, A108525, A108526, A108527, A108528, A108529, A029768.

Programs

Mathematica

Rest[CoefficientList[InverseSeries[Series[Log[(1+x)*Sqrt[1-x^2]], {x, 0, 20}], x],x] * Range[0, 20]!] (* Vaclav Kotesovec, Jan 08 2014 *)

PARI

{a(n)=n!*polcoeff(serreverse(log((1+x)*sqrt(1-x^2+O(x^(n+2))))),n)} \\ Paul D. Hanna, Sep 11 2010

Formula

E.g.f. satisfies 2*A(x) = x - 1 + A'(x) - log(1-A(x)).

From Paul D. Hanna, Sep 11 2010: (Start)

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