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Search: id:A006629
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| A006629 |
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Self-convolution 4-th power of A001764, which enumerates ternary trees.
(Formerly M3542)
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+0
9
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| 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015, 2601300, 15426840, 92431584, 558685348, 3402497504, 20858916870, 128618832864, 797168807855, 4963511449260, 31032552351570, 194743066471800, 1226232861415695
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Sum of root degrees of all noncrossing trees on nodes on a circle (from Emeric Deutsch).
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REFERENCES
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H. M. Finucan, Some decompositions of generalized Catalan numbers, pp. 275-293 of Combinatorial Mathematics IX. Proc. Ninth Australian Conference (Brisbane, August 1981). Ed. E. J. Billington, S. Oates-Williams and A. P. Street. Lecture Notes Math., 952. Springer-Verlag, 1982.
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LINKS
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Index entries for sequences related to rooted trees
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FORMULA
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a(n)=2*binomial(3n-3, n-2)/n (from Emeric Deutsch). G.f.: 3_F_2 ( [ 2, 5/3, 4/3 ]; [ 3, 5/2 ]; 27 x / 4 ).
G.f. A(x) = G(x)^4 where G(x) = 1 + x*G(x)^3 = g.f. of A001764 giving a(n)=C(3n+m-1,n)*m/(2n+m) at power m=4 with offset n=0. - Paul D. Hanna (pauldhanna(AT)juno.com), May 10 2008
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PROGRAM
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(PARI) a(n)=local(m=4); binomial(3*n+m-1, n)*m/(2*n+m) /* 4-th power of A001764 with offset n=0 */ - Paul D. Hanna (pauldhanna(AT)juno.com), May 10 2008
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CROSSREFS
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Sequence in context: A050146 A083879 A081671 this_sequence A068764 A127394 A046984
Adjacent sequences: A006626 A006627 A006628 this_sequence A006630 A006631 A006632
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KEYWORD
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nonn,easy
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AUTHOR
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Simon Plouffe (plouffe(AT)math.uqam.ca), njas
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EXTENSIONS
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More terms from James A. Sellers (sellersj(AT)math.psu.edu), Aug 21 2000
More precise definition from Paul D. Hanna (pauldhanna(AT)juno.com), May 10 2008
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