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A091481
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Number of labeled rooted 2,3 cacti (triangular cacti with bridges).
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2
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1, 2, 12, 112, 1450, 23976, 482944, 11472896, 314061948, 9734500000, 336998573296, 12888244482048, 539640296743288, 24552709165722752, 1206192446775000000, 63633506348182798336, 3587991568046845781776
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also labeled involution rooted trees.
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REFERENCES
| 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
| Index entries for sequences related to cacti
Index entries for sequences related to rooted trees
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FORMULA
| 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
| a(n) = A091485(n)*n. Cf. A032035, A091486.
Sequence in context: A124213 A143134 A185190 * A053312 A091854 A141141
Adjacent sequences: A091478 A091479 A091480 * A091482 A091483 A091484
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KEYWORD
| nonn,eigen
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AUTHOR
| Christian G. Bower (bowerc(AT)usa.net), Jan 13 2004
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