A108527 - OEIS

%I #15 Aug 11 2014 22:45:27

%S 1,3,20,229,3764,80383,2107412,65436033,2347211812,95492023811,

%T 4344109422388,218499395486909,12039757564700644,721239945304498215,

%U 46669064731537444820,3243864647191662324601,241046155271316751794596

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

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

%H Vaclav Kotesovec, <a href="/A108527/b108527.txt">Table of n, a(n) for n = 1..250</a>

%H <a href="/index/Mo#mobiles">Index entries for sequences related to mobiles</a>

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

%F a(n) ~ c * n^(n-1) / (exp(n) * r^n), where r = 0.20846306198165450115960050053484328028... and c = 0.3060161306524907981116283162103879... - _Vaclav Kotesovec_, Mar 28 2014

%t 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 *)

%o (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)}

%o for(n=1, 20, print1(a(n), ", ")) \\ _Vaclav Kotesovec_, Mar 28 2014

%Y Cf. A108521-A108529, A038037, A032188.

%K nonn

%O 1,2

%A _Christian G. Bower_, Jun 07 2005