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A034940
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Number of rooted labeled triangular cacti with 2n+1 nodes (n triangles).
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3
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1, 3, 75, 5145, 688905, 152193195, 50174679555, 23089081640625, 14140034726843025, 11119632520038117075, 109208030439676358940750, 13100477280449146440878025
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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REFERENCES
| F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Camb. 1998, p. 307. (4.2.44)
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LINKS
| Index entries for sequences related to cacti
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FORMULA
| a(n)=b(2n+1). E.g.f. of b satisfies B(x)=x*exp(B(x)^2/2).
The closed form a(n) = (2n-1)!! (2n+1)^n can be obtained from the generating function. - Noam D. Elkies (elkies(AT)math.harvard.edu), Dec 16 2002
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EXAMPLE
| E.g. a(3) = 5!! 7^3 = (1*3*5) * 343 = 5145.
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CROSSREFS
| Cf. A003080.
Sequence in context: A136328 A003690 A195263 * A183290 A089301 A037110
Adjacent sequences: A034937 A034938 A034939 * A034941 A034942 A034943
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Oct 15 1998.
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