%I A061639
%S A061639 0,1,1,1,4,10,28,85,262,829,2677,8776,29143,97825,331381,1131409,
%T A061639 3889381,13450744,46764532,163357807,573064849,2018027719,7131064045,
%U A061639 25278463756,89866690732,320328538033,1144591699069,4099050204445
%N A061639 Number of planar planted trees with n non-root nodes and every 2-valent 
               node isolated.
%C A061639 Isolated 2-valent node is a 2-valent node non-adjacent to any other 2-valent 
               node.
%D A061639 I. P. Goulden and D. M. Jackson, Combinatorial Enumeration, Wiley, N.Y., 
               1983, (Problem 2.7.4).
%F A061639 a(n) = Sum_{m=0..n-1} Sum_{i=0..n-m-1} (-1)^i/(m+1)*binomial(2*m, m)*binomial(m+i, 
               i)*binomial(m+i+1, n-m-i-1). G.f.: 1/2*(1-sqrt(1-4*(x+x^2)/(1+x+x^2))).
%Y A061639 Sequence in context: A091468 A103457 A083587 this_sequence A008995 A111236 
               A164361
%Y A061639 Adjacent sequences: A061636 A061637 A061638 this_sequence A061640 A061641 
               A061642
%K A061639 nonn
%O A061639 0,5
%A A061639 Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 13 2001