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A035102 Composite binary rooted trees with external nodes. 2


%S 0,0,1,0,4,0,9,4,28,0,98,0,264,56,869,0,3016,0,9822,528,33592,0,

%T 119530,196,416024,5712,1486724,0,5369336,0,19392637,67184,70715340,

%U 3696,259535958,0

%N Composite binary rooted trees with external nodes.

%C If a,b are binary trees, a.b is equal to tree b where a copy of a is put on each of b's external node. This is non-commutative but associative. A binary tree a is prime if it is different from the 1 node tree and if a=b.c implies that b or c is equal to the 1 node tree.

%H <a href="/index/Ro#rooted">Index entries for sequences related to rooted trees</a>

%F A035010(n)+A035102(n)=Catalan(n-1)=A000108(n-1).

%t (* b = A035010 *) b[n_] := b[n] = CatalanNumber[n-1] - Sum[If[Divisible[n, d1], d2 = n/d1; b[d1]*CatalanNumber[d2-1], 0], {d1, 2, n-1}]; b[2] = 1; a[n_] := a[n] = CatalanNumber[n-1] - b[n]; Table[a[n], {n, 2, 37}] (* _Jean-Fran├žois Alcover_, Jul 17 2012, after formula *)

%Y Cf. A035010.

%K nonn

%O 2,5

%A Bernard AMERLYNCK (B.Amerlynck(AT)ulg.ac.be)

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Last modified September 22 00:41 EDT 2020. Contains 337276 sequences. (Running on oeis4.)