A103944 Number of rooted unicursal n-edge maps in the plane (planar with a distinguished outside face).

1, 10, 93, 836, 7355, 63750, 546553, 4646920, 39250935, 329789450, 2758868981, 22995369996, 191074697203, 1583463268366, 13092015636465, 108024564809744, 889730213085167, 7316434446188562, 60078376613838829, 492692533579612180

Offset: 1

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

• Vincenzo Librandi, Table of n, a(n) for n = 1..200
• 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. A069720, A103945.

Programs

Mathematica

Flatten[{1,Table[n*Binomial[2n,n]*Sum[Binomial[n-2,k]*(1/(n+1+k)+n/(n+2+k)),{k,0,n-2}],{n,2,20}]}] (* Vaclav Kotesovec, Oct 17 2012 *)

Formula

a(n)=n*binomial(2n, n)sum_{i=0..n-2} binomial(n-2, i)(1/(n+1+i)+n/(n+2+i)), for n>1.

Recurrence: (n-1)*a(n) = 3*(3*n-4)*a(n-1) - 6*(n-9)*a(n-2) - 8*(2*n-5)*a(n-3). - Vaclav Kotesovec, Oct 17 2012

a(n) ~ 8^n*sqrt(n)/(6*sqrt(Pi)). - Vaclav Kotesovec, Oct 17 2012