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%I A113949 #4 Mar 30 2012 18:53:07
%S A113949 1,1,0,1,2,1,1,0,3,0,1,2,5,8,1,1,0,11,0,16,0,1,2,21,128,232,64,1,1,0,
%T A113949 43,0,5680,0,264,0,1,2,85,3968,132448,581696,144504,1580,1,1,0,171,0,
%U A113949 3189184,0,107174448,0,10648,0,1,2,341,140288,76426624,8297164544
%N A113949 Number of n-fold branched coverings of the projective plane with r cyclic branch points (n,r>=1); array read by downward antidiagonals.
%C A113949 The second column is A113947.
%D A113949 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 A113949 E.g. for n=7 and r>=1, a(7, r)=(2*720^(r-1)+(-1)^r*2*120^(r-1)+2*48^(r-1)+(-1)^r*36^(r-1)+6^r)/7 (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 A113949 The array begins:
%e A113949 1 1 1 1 1 1 1 ...
%e A113949 0 2 0 2 0 2 0 ...
%e A113949 1 3 5 11 21 43 85 ...
%e A113949 0 8 0 128 0 3968 0 ...
%Y A113949 Cf. A113947, A113950.
%K A113949 nonn,tabl
%O A113949 1,5
%A A113949 _Valery A. Liskovets_, Nov 10 2005

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