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
KEYWORD
easy,nonn
AUTHOR
Valery A. Liskovets, Mar 17 2005
STATUS
approved