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A103945
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Number of rooted dual-unicursal n-edge maps in the plane (planar with a distinguished outside face).
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1
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2, 14, 107, 844, 6757, 54522, 441863, 3589880, 29206025, 237780982, 1936486411, 15771410420, 128431734797, 1045618229234, 8510270668815, 69241255165936, 563154350637073, 4578526894227438, 37209886138826771, 302291556342169580
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OFFSET
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1,1
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REFERENCES
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V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.
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LINKS
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Table of n, a(n) for n=1..20.
V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.
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FORMULA
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a(n)=(n+2)*A069720(n)-A103944(n).
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MATHEMATICA
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A069720[n_] := 2^(n-1) Binomial[2n-1, n];
A103944[n_] := If[n == 1, 1, n Binomial[2n, n] Sum[Binomial[n-2, k] (1/(n + 1 + k) + n/(n + 2 + k)), {k, 0, n-2}]];
a[n_] := (n+2) A069720[n] - A103944[n];
Array[a, 20] (* Jean-François Alcover, Aug 28 2019 *)
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CROSSREFS
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Cf. A069720, A103944.
Sequence in context: A074618 A108436 A088754 * A111713 A144278 A359108
Adjacent sequences: A103942 A103943 A103944 * A103946 A103947 A103948
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KEYWORD
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easy,nonn
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AUTHOR
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Valery A. Liskovets, Mar 17 2005
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STATUS
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approved
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