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%I #5 Sep 12 2018 15:10:35
%S 1,1,3,7,21,75,277,1083,4419,18493,77729,332557,1444477,6307225,
%T 27912147,123878207,554733045,2492087531,11280537097,51120499279,
%U 233319480419,1065835004917,4895443823281,22505853359485,103958158302085,480365303903637,2229412587062123
%N Number of series-reduced plane trees with n leaves such that each branch directly under any given node has a different number of leaves.
%e The a(4) = 7 plane trees:
%e (oooo)
%e (o(ooo))
%e ((ooo)o)
%e (o(o(oo)))
%e (o((oo)o))
%e ((o(oo))o)
%e (((oo)o)o)
%t b[n_]:=b[n]=1+Sum[Times@@b/@f,{f,Join@@Permutations/@Select[IntegerPartitions[n],And[Length[#]>1,UnsameQ@@#]&]}];
%t Array[b,30]
%Y Cf. A000108, A001003, A007853, A074206, A118376, A273873, A277130, A281113, A304173, A304175, A319122.
%K nonn
%O 1,3
%A _Gus Wiseman_, Sep 11 2018
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