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0, 0, 0, 1, 30, 705, 15960, 370125, 8998290, 231416325, 6314962500, 182894567625, 5615811951750, 182497749258825, 6264206330382000, 226636350724909125, 8624703350821808250, 344535241891693978125, 14419858385821910521500
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,5
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COMMENTS
| a(n) = A035342(n,4).
a(n), n>=4, enumerates unordered n-vertex forests composed of four plane (ordered) increasingly labeled ternary (3-ary) trees. See A001147 (number of increasing ternary trees) and a D. Callan comment there. For a picture of some ternary trees see a W. Lang link under A001764.
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FORMULA
| a(n) = n!*A045894(n-4)/(4!*2^(n-4)), n >= 4; E.g.f. ((x*c(x/2)/(1-2*x)^(1/2))^4)/4!, where c(x) = g.f. for Catalan numbers A000108, a(0) := 0.
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EXAMPLE
| a(5)=30 increasing ternary 4-forest with n=5 vertices: there are three such 4-forests (three one vertex trees together with any of the three different 2-vertex trees) each with 10 increasing labelings. W. Lang, Sep 14 2007.
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CROSSREFS
| Cf. A035342, A045894.
Sequence in context: A152499 A027475 A180801 * A122186 A166840 A166828
Adjacent sequences: A035517 A035518 A035519 * A035521 A035522 A035523
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KEYWORD
| easy,nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de)
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