%I #10 Sep 20 2018 15:16:44
%S 1,1,1,2,4,9,23,62,164,449,1263,3636,10500,30859,90895,271178,810918,
%T 2447715,7406439,22589066,68974940,211989119,652180385,2016872920,
%U 6242930834,19412141273,60390977831,188627507266
%N Number of rooted planar trees where any 2 subtrees extending from same node have a different number of nodes.
%H Andrew Howroyd, <a href="/A032010/b032010.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 "CFK" (Necklace, size, unlabeled) transform of A032009 (shifted right one place)
%o (PARI)
%o AFK(v)={apply(p->subst(serlaplace(y^0*p), y, 1), Vec(-1+prod(k=1, #v, 1 + v[k]*x^k*y + O(x*x^#v)), -#v))}
%o CFK(v)={apply(p->subst(serlaplace(p/y),y,1), Vec(-1+prod(k=1, #v, 1 + v[k]*x^k*y + O(x*x^#v)), -#v))}
%o seq(n)={my(v=[1]); for(i=3, n, v=concat([1], AFK(v))); concat([1], CFK(v))} \\ _Andrew Howroyd_, Sep 20 2018
%K nonn
%O 1,4
%A _Christian G. Bower_