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A035010
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Prime binary rooted trees with n external nodes.
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2
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1, 2, 4, 14, 38, 132, 420, 1426, 4834, 16796, 58688, 208012, 742636, 2674384, 9693976, 35357670, 129641774, 477638700, 1767253368, 6564119892, 24466233428, 91482563640, 343059494120, 1289904147128, 4861945985428
(list; graph; refs; listen; history; internal format)
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OFFSET
| 2,2
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COMMENTS
| 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.
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REFERENCES
| B. Amerlynck, Ite're'es d'exponentielles: aspects combinatoires et arithme'tiques, Me'moire de licence, Univ. Libre de Bruxelles (1998).
V. Blondel, Structured numbers: properties of a hierarchy of operations on binary trees, Acta Informatica, vol. 35 (1998), pp. 1-15.
V. Blondel, Operations on binary trees, Comptes Rendus de l'Acad. des Sciences de Paris - Ser. I, 321, pp. 491-494, 1995.
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LINKS
| Index entries for sequences related to rooted trees
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FORMULA
| a(n)=Cat_{n-1} - sum_{d_1.d_2=n and 1<d_1<n}a(d_1).Cat_{d_2-1} where Cat_n = n-th Catalan number (A000108).
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EXAMPLE
| a(4) = Cat_3 - sum_{d_1.d_2=4}a(d_1)Cat_{d_2-1} = 5 - a(2)Cat_1 = 5 - 1 = 4
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MATHEMATICA
| a[n_] := a[n] = CatalanNumber[n-1] - Sum[If[Divisible[n, d1], d2 = n/d1; a[d1]*CatalanNumber[d2-1], 0], {d1, 2, n-1}]; a[2] = 1; Table[a[n], {n, 2, 26}] (* From Jean-François Alcover, Oct 25 2011, after formula *)
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CROSSREFS
| Cf. A035102.
Sequence in context: A006611 A007462 A053623 * A055540 A006252 A079995
Adjacent sequences: A035007 A035008 A035009 * A035011 A035012 A035013
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KEYWORD
| nice,easy,nonn
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AUTHOR
| Bernard Amerlynck (B.Amerlynck(AT)ulg.ac.be)
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EXTENSIONS
| More terms from Christian G. Bower (bowerc(AT)usa.net)
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