%I #10 Sep 20 2018 16:26:15
%S 1,1,1,2,4,9,23,62,167,461,1309,3784,11018,32431,96294,288246,868107,
%T 2629499,8005166,24482202,75177313,231697259,716488213,2222381516,
%U 6912569477,21556270329,67380727837,211080434346
%N Number of rooted planar trees (n+1 nodes) where any 2 subtrees extending from same node are different.
%H Andrew Howroyd, <a href="/A032028/b032028.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 "CGK" (necklace, elements, unlabeled) transform of A032027 (shifted right one place).
%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 CGK(v)={apply(p->subst(serlaplace(p/y),y,1), Vec(prod(k=1, #v, (1 + x^k*y + O(x*x^#v))^v[k])-1, -#v))}
%o seq(n)={my(v=[1]); for(i=3, n, v=concat([1], AGK(v))); concat([1], CGK(v))} \\ _Andrew Howroyd_, Sep 20 2018
%K nonn
%O 1,4
%A _Christian G. Bower_