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A328121
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Number of unrooted level-1 phylogenetic networks (also called galled trees) with (n+1) labeled leaves.
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5
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1, 2, 15, 192, 3450, 79740, 2252880, 75227040, 2898481320, 126570502800, 6177380517000, 333231084648000, 19687828831070400, 1264341183311606400, 87691200344603856000, 6532556443068591936000, 520205544912884502672000, 44098092640676115673632000, 3964782594938523231457584000
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,2
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LINKS
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Mathilde Bouvel, Philippe Gambette and Marefatollah Mansouri, Maple worksheet
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FORMULA
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Semple and Steele provide a summation formula for a(n) (see their Theorem 4).
Bouvel, Gambette and Mansouri provide (among other additional results) an equation for the associated exponential generating function, and an asymptotic estimate of a(n). See their Section 4.
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EXAMPLE
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a(4) = 192 is the number of unrooted level-1 phylogenetic networks with 5 labeled leaves
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MAPLE
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# see links section
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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