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Search: id:A113948
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| A113948 |
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Number of non-equivalent (2n+1)-fold branched coverings of the Klein bottle with one cyclic branch point. |
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+0
3
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| 1, 5, 44, 1266, 72636, 6652810, 889574412, 163459302788, 39520825344016, 12164510040883218, 4644631106520877974, 2154334728240414720022, 1193170003333152768100020, 777776389315596583864343748
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OFFSET
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0,2
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COMMENT
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No such covering of even multiplicity exists.
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REFERENCES
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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.
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FORMULA
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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.
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CROSSREFS
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Cf. A113947, A113950.
Sequence in context: A052803 A048940 A058792 this_sequence A096763 A003185 A027801
Adjacent sequences: A113945 A113946 A113947 this_sequence A113949 A113950 A113951
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KEYWORD
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nonn
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AUTHOR
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Valery A. Liskovets (liskov(AT)im.bas-net.by), Nov 10 2005
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