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A113948
Number of non-equivalent (2n+1)-fold branched coverings of the Klein bottle with one cyclic branch point.
2
1, 5, 44, 1266, 72636, 6652810, 889574412, 163459302788, 39520825344016, 12164510040883218, 4644631106520877974, 2154334728240414720022, 1193170003333152768100020, 777776389315596583864343748
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
Sequence in context: A360988 A058792 A374583 * A215517 A215584 A262116
KEYWORD
nonn
AUTHOR
Valery A. Liskovets, Nov 10 2005
STATUS
approved