cp's OEIS Frontend

A108525 Number of increasing ordered rooted trees with n generators.

%I A108525 #17 Feb 20 2014 17:14:45
%S A108525 1,3,27,429,9609,277107,9772803,407452221,19604840481,1069202914083,
%T A108525 65177482634667,4391636680582029,324102772814580729,
%U A108525 25999541378465556627,2252597527900572815763,209625760563134613131421
%N A108525 Number of increasing ordered rooted trees with n generators.
%C A108525 A generator is a leaf or a node with just one child.
%C A108525 In an increasing rooted tree, nodes are numbered and numbers increase as you move away from root.
%H A108525 Vaclav Kotesovec, <a href="/A108525/b108525.txt">Table of n, a(n) for n = 1..200</a>
%H A108525 <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F A108525 E.g.f. satisfies: A(x) = -1 + 2*A'(x) - A'(x)/(1-A(x))^2, corrected by _Vaclav Kotesovec_ and _Paul D. Hanna_, Feb 20 2014
%F A108525 A(x) = Series_Reversion( (log(1-x) + 7*log(1+x) + 2/(x-1))/4 + 1/2). - _Vaclav Kotesovec_, Feb 20 2014
%F A108525 a(n) ~ sqrt(4-sqrt(2)) * 2^(3*n-13/4) * n^(n-1) / (exp(n) * (4-4*sqrt(2)-log(2)+14*log(2-1/sqrt(2)))^(n-1/2)). - _Vaclav Kotesovec_, Feb 20 2014
%t A108525 Rest[CoefficientList[InverseSeries[Series[(Log[1-x]+7*Log[1+x]+2/(x-1))/4+1/2,{x,0,20}],x],x]*Range[0,20]!] (* _Vaclav Kotesovec_, Feb 20 2014 *)
%o A108525 (PARI) {a(n)=local(A=x); for(i=1, n, A=intformal((A-1)^2 * (1+A) /(1 - 4*A + 2*A^2)+O(x^n))); n!*polcoeff(A, n)};
%o A108525 for(n=1, 20, print1(a(n), ", ")); /* _Vaclav Kotesovec_, Feb 20 2014 */
%Y A108525 Cf. A108521-A108529, A001147.
%K A108525 nonn
%O A108525 1,2
%A A108525 _Christian G. Bower_, Jun 07 2005