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A342983
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Number of tree-rooted planar maps with n+1 vertices and n+1 faces.
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2
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1, 6, 280, 23100, 2522520, 325909584, 47117214144, 7383099180600, 1229149289511000, 214527522662653200, 38887279926227853120, 7271332144993605081120, 1395321310426879365566400, 273697641660657106322640000, 54708248601655917595233984000
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OFFSET
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0,2
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COMMENTS
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The number of edges is 2*n.
Also, a(n) is the number of discrete walks that start and stop at the origin, never pass below the x-axis nor to the left of the y-axis, and, in any order, have n steps that increment x, n steps that decrement x, n steps that increment y, and n steps that decrement y. It is in this sense a way to generalize the 2n-step one-dimensional walks counted by A000108 to a count in two dimensions. Proof: There are A001448(n) ways to interleave two length-2n Dyck words (A000108(n)^2) - Lee A. Newberg, Nov 17 2023
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LINKS
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FORMULA
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a(n) = (4*n)!/(n!*(n+1)!)^2.
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PROG
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(PARI) a(n) = {(4*n)!/(n!*(n+1)!)^2}
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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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