A108527 Number of labeled mobiles (cycle rooted trees) with n generators.

1, 3, 20, 229, 3764, 80383, 2107412, 65436033, 2347211812, 95492023811, 4344109422388, 218499395486909, 12039757564700644, 721239945304498215, 46669064731537444820, 3243864647191662324601, 241046155271316751794596

Offset: 1

Author

Christian G. Bower, Jun 07 2005

Keywords

• nonn

Comments

A generator is a leaf or a node with just one child.

Links

• Vaclav Kotesovec, Table of n, a(n) for n = 1..250
• Index entries for sequences related to mobiles

Crossrefs

Cf. A108521-A108529, A038037, A032188.

Programs

Mathematica

nmax=20; c[0]=0; A[x_]:=Sum[c[k]*x^k/k!,{k,0,nmax}]; Array[c,nmax]/.Solve[Rest[CoefficientList[Series[x-1-Log[1-A[x]]-(2-x)*A[x],{x,0,nmax}],x]]==0][[1]] (* Vaclav Kotesovec, Mar 28 2014 *)

PARI

{a(n)=local(A=x+O(x^n)); for(i=0, n, A=intformal((1-A^2)/(1-x-2*A+x*A)+O(x^n))); n!*polcoeff(A, n)}
for(n=1, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Mar 28 2014

Formula

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

a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.20846306198165450115960050053484328028... and c = 0.3060161306524907981116283162103879... - Vaclav Kotesovec, Mar 28 2014