A103938 Number of rooted non-separable n-edge maps in the plane (planar with a distinguished outside face).

3, 2, 5, 18, 77, 364, 1836, 9690, 52877, 296010, 1690845, 9817080, 57769740, 343806368, 2065802056, 12515350122, 76367432013, 468922828150, 2895381678735, 17966214519330, 111977263221285, 700704492237540, 4400559613086000, 27727270719559320, 175230257041962252

Offset: 1

Author

Valery A. Liskovets, Mar 17 2005

Keywords

• nonn
• easy

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

• V. A. Liskovets and T. R. Walsh, Counting unrooted maps on the plane, Advances in Applied Math., 36, No.4 (2006), 364-387.

Crossrefs

Cf. A000139, A001764, A006013.

Programs

Mathematica

a[n_] := (n+2)(3(n-1))!/((2n-1)! n!);
Array[a, 30] (* Jean-François Alcover, Aug 29 2019 *)

Formula

a(n) = (n+2)*A000139(n)/2.

From Peter Bala, Feb 07 2022: (Start)

a(n) = 4*A001764(n-1) - A006013(n-1).

a(n) = (3*n+6)*(3*n-4)*(3*n-5)/(n*(2*n-1)*(2*n+2))*a(n-1).

O.g.f.: A(x) = x*T(x)*(4 - T(x)), where T(x) = 1 + x*T(x)^3 is the g.f. of A001764. (End)

Extensions

More terms from Jean-François Alcover, Aug 29 2019