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Number of n-fold branched coverings of the Klein bottle with r cyclic branch points (n,r>=1); array read by downward antidiagonals.
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%I #4 Mar 30 2012 18:53:07

%S 1,1,0,1,4,5,1,0,13,0,1,4,23,104,44,1,0,49,0,1256,0,1,4,95,2720,27344,

%T 30608,1266,1,0,193,0,666656,0,1071540,0,1,4,383,93824,15911744,

%U 415444544,743214744

%N Number of n-fold branched coverings of the Klein bottle with r cyclic branch points (n,r>=1); array read by downward antidiagonals.

%C The odd bisection of the first column is A113948.

%D 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.

%F E.g. for n=7 and r>=1, a(7, r)=2*720^r+(-1)^r*2*120^r+2*48^r+(-1)^r*36^r+6^r (more generally, a(7, r, h)=7^(h-2)*(2*720^m+(-1)^r*2*120^m+2*48^m+(-1)^r*36^m+6^r) for 7-sheeted coverings of the non-orientable surface of genus h>=1, where m=h+r-2).

%e The array begins:

%e 1 1 1 1 1 1 ...

%e 0 4 0 4 0 4 ...

%e 5 13 23 49 95 193 ...

%e 0 104 0 2720 0 93824 ...

%Y Cf. A113948, A113949.

%K nonn,tabl

%O 1,5

%A _Valery A. Liskovets_, Nov 10 2005