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A103944
Number of rooted unicursal n-edge maps in the plane (planar with a distinguished outside face).
2
1, 10, 93, 836, 7355, 63750, 546553, 4646920, 39250935, 329789450, 2758868981, 22995369996, 191074697203, 1583463268366, 13092015636465, 108024564809744, 889730213085167, 7316434446188562, 60078376613838829, 492692533579612180
OFFSET
1,2
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.
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
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 *)
CROSSREFS
Sequence in context: A287829 A265242 A262173 * A190989 A375246 A224696
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Mar 17 2005
STATUS
approved