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A103945 Number of rooted dual-unicursal n-edge maps in the plane (planar with a distinguished outside face). 1
2, 14, 107, 844, 6757, 54522, 441863, 3589880, 29206025, 237780982, 1936486411, 15771410420, 128431734797, 1045618229234, 8510270668815, 69241255165936, 563154350637073, 4578526894227438, 37209886138826771, 302291556342169580 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

V. A. Liskovets and T. R. Walsh, Enumeration of unrooted maps on the plane, Rapport technique, UQAM, No. 2005-01, Montreal, Canada, 2005.

LINKS

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.

FORMULA

a(n)=(n+2)*A069720(n)-A103944(n).

MATHEMATICA

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-Fran├žois Alcover, Aug 28 2019 *)

CROSSREFS

Cf. A069720, A103944.

Sequence in context: A074618 A108436 A088754 * A111713 A144278 A214766

Adjacent sequences:  A103942 A103943 A103944 * A103946 A103947 A103948

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Mar 17 2005

STATUS

approved

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Last modified January 21 03:16 EST 2021. Contains 340332 sequences. (Running on oeis4.)