OFFSET
0,3
COMMENTS
Counts cycles of objects where the individual objects are anything enumerated by the Catalan numbers C_1, C_2, ...
The number of unrooted two-face n-edge maps in the plane (planar with a distinguished outside face). - Valery A. Liskovets, Mar 17 2005
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..200
P. Flajolet and M. Soria, The Cycle Construction In SIAM J. Discr. Math., vol. 4 (1), 1991, pp. 58-60.
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) = (1/n) * Sum_{d|n} phi(n/d) * A000346(d-1) for n>0. - Andrew Howroyd, Apr 02 2017
MATHEMATICA
max = 25; f[x_] := (1 - Sqrt[1 - 4*x])/(2*x) - 1; gf = Sum[(EulerPhi[k]/k)*Log[1 - f[x^k]], {k, 1, max}]; CoefficientList[ Series[-gf, {x, 0, max}], x] (* Jean-Fran�ois Alcover, Jan 21 2013 *)
PROG
(PARI)
a(n) = sumdiv(n, d, eulerphi(n/d)*(2^(2*d-1) - binomial(2*d-1, d)))/n; \\ Andrew Howroyd, Apr 02 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Apr 05 2001
STATUS
approved