%I #10 Sep 20 2018 16:28:23
%S 2,2,8,46,276,1836,12712,90610,661652,4922404,37178736,284330552,
%T 2197474456,17136206984,134667604360,1065457242054,8479671583004,
%U 67841927540372,545314544677904,4401667141277988
%N Number of series-reduced planted planar trees with n leaves of 2 colors where any 2 subtrees extending from the same node are different.
%H Andrew Howroyd, <a href="/A032030/b032030.txt">Table of n, a(n) for n = 1..200</a>
%H C. G. Bower, <a href="/transforms2.html">Transforms (2)</a>
%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>
%F Doubles (index 2+) under "AGK" (ordered, elements, unlabeled) transform.
%o (PARI)
%o AGK(v)={apply(p->subst(serlaplace(y^0*p),y,1), Vec(prod(k=1, #v, (1 + x^k*y + O(x*x^#v))^v[k])-1, -#v))}
%o seq(n)={my(v=[2]); for(i=2, n, v=concat(v, AGK(concat(v,[0]))[i])); v} \\ _Andrew Howroyd_, Sep 20 2018
%K nonn
%O 1,1
%A _Christian G. Bower_