A113947 Number of non-equivalent n-fold branched coverings of the projective plane with two cyclic branch points.

1, 2, 3, 8, 16, 64, 264, 1580, 10648, 84320, 750380, 7455312, 81566928, 974988768, 12636692720, 176505029160, 2642791002368, 42224138928712, 716984262871596, 12893605560786944

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..450

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.

Formula

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.

Mathematica

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 *)

Crossrefs

Cf. A113948, A113949.

Sequence in context: A331679 A277346 A005648 * A102008 A200083 A210701

Adjacent sequences: A113944 A113945 A113946 * A113948 A113949 A113950

Keyword

nonn

Author

Valery A. Liskovets, Nov 10 2005

Status

approved