OFFSET
0,4
LINKS
Danny Rorabaugh, Table of n, a(n) for n = 0..2500
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 790
FORMULA
G.f.: (x/(x-1))*Sum_{j>=1} (A000010(j)/j)*log((x^j-1)/(2*x^j-1)).
a(n) ~ 2^n/n * (1 + 2/n + 6/n^2 + 26/n^3 + 150/n^4 + 1082/n^5 + 9366/n^6 + 94586/n^7 + 1091670/n^8 + 14174522/n^9 + 204495126/n^10 + ...), for coefficients see A000629. - Vaclav Kotesovec, Jun 03 2019
MAPLE
spec := [S, {B=Cycle(C), C=Sequence(Z, 1 <= card), S=Prod(C, B)}, unlabeled]: seq(combstruct[count](spec, size=n), n=0..20);
h := n -> add(numtheory:-phi(j)/j*log((x^j-1)/(2*x^j-1)), j=1..n):
seq(coeff(series((x/(1-x))*h(n), x, n+1), x, n), n=0..36); # Peter Luschny, Oct 25 2015
MATHEMATICA
m = 40;
gf = (x/(1-x))*Sum[EulerPhi[j]/j*Log[(x^j-1)/(2*x^j-1)], {j, 1, m}] + O[x]^m;
CoefficientList[gf, x] (* Jean-François Alcover, Jun 03 2019 *)
PROG
(Sage) var('x'); a = lambda n: taylor(x/(1-x) * sum([taylor(euler_phi(i)/i * log((x^i - 1)/(2*x^i - 1)), x, 0, n) for i in range(1, n+1)]), x, 0, n).coefficient(x^n) # Danny Rorabaugh, Oct 25 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
encyclopedia(AT)pommard.inria.fr, Jan 25 2000
EXTENSIONS
More terms from Danny Rorabaugh, Oct 25 2015
STATUS
approved