A103939 Number of unrooted Eulerian n-edge maps in the plane (planar with a distinguished outside face).

1, 1, 3, 8, 32, 136, 722, 3924, 22954, 138316, 860364, 5472444, 35503288, 234070648, 1564945158, 10589356592, 72412611194, 499788291616, 3478059566250, 24383023246284, 172074483068320, 1221654305104920, 8720583728414354, 62560709120463028, 450854177292364660

Offset: 0

Author

Valery A. Liskovets, Mar 17 2005

Keywords

• easy
• nonn

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

• Andrew Howroyd, Table of n, a(n) for n = 0..500
• 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. A052701, A103940, A069727.

Programs

Mathematica

a[n_] := (1/(2n)) (2^n Binomial[2n, n]/(n+1) + Sum[Boole[0Jean-François Alcover, Aug 28 2019 *)

PARI

a(n)={if(n==0, 1, sumdiv(n, d, if(dAndrew Howroyd, Mar 29 2021

Formula

For n > 0, a(n) = (1/(2n))*(2^n*binomial(2n, n)/(n+1) + Sum_{0A000010.

Extensions

a(0)=1 prepended and terms a(21) and beyond from Andrew Howroyd, Mar 29 2021