OFFSET
0,2
COMMENTS
No such covering of even multiplicity exists.
REFERENCES
J. H. Kwak, A. Mednykh and V. Liskovets, Enumeration of branched coverings of nonorientable surfaces with cyclic branch points, SIAM J. Discrete Math., Vol. 19, No. 2 (2005), 388-398.
FORMULA
a(n)=2*sum_{k|(2n+1)}k!*((2n+1)/k)^(k-1)*phi((2n+1)/k)/(k+1) where phi(n) is the Euler function A000010.
a(n) ~ sqrt(Pi) * 2^(2*n + 2) * n^(2*n + 1/2) / exp(2*n). - Vaclav Kotesovec, Oct 27 2024
MATHEMATICA
Table[2*Sum[k!*((2*n + 1)/k)^(k-1) * EulerPhi[(2*n + 1)/k] / (k+1), {k, Divisors[2*n + 1]}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 27 2024 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Valery A. Liskovets, Nov 10 2005
STATUS
approved