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A113947 Number of non-equivalent n-fold branched coverings of the projective plane with two cyclic branch points. 3
1, 2, 3, 8, 16, 64, 264, 1580, 10648, 84320, 750380, 7455312, 81566928, 974988768, 12636692720, 176505029160, 2642791002368, 42224138928712, 716984262871596, 12893605560786944 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois Alcover, Oct 05 2016 *)

CROSSREFS

Cf. A113948, A113949.

Sequence in context: A204516 A277346 A005648 * A102008 A200083 A210701

Adjacent sequences:  A113944 A113945 A113946 * A113948 A113949 A113950

KEYWORD

nonn

AUTHOR

Valery A. Liskovets, Nov 10 2005

STATUS

approved

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Last modified January 28 06:29 EST 2020. Contains 331317 sequences. (Running on oeis4.)