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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 (list; graph; refs; listen; history; text; internal format)
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

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.

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

Cf. A069720, A103945.

Sequence in context: A287829 A265242 A262173 * A190989 A224696 A099295

Adjacent sequences:  A103941 A103942 A103943 * A103945 A103946 A103947

KEYWORD

easy,nonn

AUTHOR

Valery A. Liskovets, Mar 17 2005

STATUS

approved

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Last modified November 24 18:11 EST 2020. Contains 338616 sequences. (Running on oeis4.)