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A102755 Number of asymmetric (or identity) oriented trees with n nodes.

%I A102755 #14 Feb 24 2015 04:37:25
%S A102755 1,1,1,4,10,37,135,522,2060,8430,35115,149286,644456,2821835,12503878,
%T A102755 56001856,253174451,1154179790,5301178673,24513058220,114042743290,
%U A102755 533510321377,2508491383101,11849321038092,56211286929146,267707017974770,1279602152054934
%N A102755 Number of asymmetric (or identity) oriented trees with n nodes.
%H A102755 Alois P. Heinz, <a href="/A102755/b102755.txt">Table of n, a(n) for n = 1..500</a>
%F A102755 G.f.: B(x)-B(x)^2, where B(x) is g.f. for A005753.
%F A102755 a(n) ~ c * d^n / n^(5/2), where d = A246312 = 5.249032491228170579164952216..., c = 0.17807103914078424643862998... . - _Vaclav Kotesovec_, Aug 25 2014
%p A102755 b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0,
%p A102755       add(binomial(2*b(i-1$2), j)*b(n-i*j, i-1), j=0..n/i)))
%p A102755     end:
%p A102755 a:= n-> b(n-1$2)-add(b(j-1$2)*b(n-j-1$2), j=1..n-1):
%p A102755 seq(a(n), n=1..35);  # _Alois P. Heinz_, Aug 01 2013
%t A102755 b[n_, i_] := b[n, i] = If[n == 0, 1, If[i<1, 0, Sum[Binomial[2*b[i-1, i-1], j]*b[n - i*j, i-1], {j, 0, n/i}]]] // FullSimplify; a[n_] := b[n-1, n-1] - Sum[b[j-1, j-1]*b[n-j-1, n-j-1], {j, 1, n-1}]; Table[a[n], {n, 1, 35}] (* _Jean-François Alcover_, Feb 24 2015, after _Alois P. Heinz_ *)
%Y A102755 Cf. A005753 = number of asymmetric (or identity) rooted oriented trees with n nodes.
%Y A102755 Cf. A246312.
%K A102755 nonn
%O A102755 1,4
%A A102755 _Vladeta Jovovic_, Feb 10 2005