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%I A113947 #15 Oct 27 2024 04:44:56
%S A113947 1,2,3,8,16,64,264,1580,10648,84320,750380,7455312,81566928,974988768,
%T A113947 12636692720,176505029160,2642791002368,42224138928712,
%U A113947 716984262871596,12893605560786944
%N A113947 Number of non-equivalent n-fold branched coverings of the projective plane with two cyclic branch points.
%H A113947 G. C. Greubel, <a href="/A113947/b113947.txt">Table of n, a(n) for n = 1..450</a>
%H A113947 J. H. Kwak, A. Mednykh and V. Liskovets, <a href="https://doi.org/10.1137/S0895480103424043">Enumeration of branched coverings of nonorientable surfaces with cyclic branch points</a>, SIAM J. Discrete Math., Vol. 19, No. 2 (2005), 388-398.
%F A113947 a(n) = (1/n)*Sum_{k|n} gcd(2, n/k)*phi(n/k)^2*(n/k)^(k-1) * Sum_{i=0..k-1} i!*(k-i-1)! where phi(n) is the Euler function A000010.
%F A113947 a(n) ~ 2*n!/n^2. - _Vaclav Kotesovec_, Oct 27 2024
%t A113947 a[n_] := 1/n DivisorSum[n, GCD[2, n/#]*EulerPhi[n/#]^2*(n/#)^(#-1) Sum[i! * (#-i- 1)!, {i, 0, #-1}]&]; Array[a, 20] (* _Jean-François Alcover_, Oct 05 2016 *)
%Y A113947 Cf. A113948, A113949.
%K A113947 nonn
%O A113947 1,2
%A A113947 _Valery A. Liskovets_, Nov 10 2005

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