A113948 Number of non-equivalent (2n+1)-fold branched coverings of the Klein bottle with one cyclic branch point.

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.

Links

Table of n, a(n) for n=0..13.

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.

Crossrefs

Cf. A113947, A113950.

Sequence in context: A360988 A058792 A374583 * A215517 A215584 A262116

Adjacent sequences: A113945 A113946 A113947 * A113949 A113950 A113951

Keyword

nonn

Author

Valery A. Liskovets, Nov 10 2005

Status

approved