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.
a(n) ~ 2*n!/n^2. - Vaclav Kotesovec, Oct 27 2024
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
KEYWORD
nonn
AUTHOR
Valery A. Liskovets, Nov 10 2005
STATUS
approved