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Search: id:A091481
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| A091481 |
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Number of labeled rooted 2,3 cacti (triangular cacti with bridges). |
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+0
3
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| 1, 2, 12, 112, 1450, 23976, 482944, 11472896, 314061948, 9734500000, 336998573296, 12888244482048, 539640296743288, 24552709165722752, 1206192446775000000, 63633506348182798336, 3587991568046845781776
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also labeled involution rooted trees.
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REFERENCES
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F. Bergeron, G. Labelle and P. Leroux, Combinatorial Species and Tree-Like Structures, Cambridge, 1998, pg 185 (3.1.84)
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LINKS
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Index entries for sequences related to cacti
Index entries for sequences related to rooted trees
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FORMULA
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E.g.f. A(x) satisfies A(x) = x*exp(A(x)+A(x)^2/2)
a(n) = i^(n-1)*n^((n-1)/2)*He_{n-1}(-sqrt(-n)), i=sqrt(-1), He_k unitary Hermite polynomial (cf. A066325)
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CROSSREFS
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a(n) = A091485(n)*n. Cf. A032035, A091486.
Adjacent sequences: A091478 A091479 A091480 this_sequence A091482 A091483 A091484
Sequence in context: A009232 A124213 A143134 this_sequence A053312 A091854 A141141
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KEYWORD
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nonn,eigen
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Jan 13 2004
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