A052825 A simple grammar.

0, 0, 1, 3, 6, 11, 18, 31, 50, 85, 144, 251, 438, 789, 1420, 2601, 4792, 8907, 16618, 31219, 58814, 111301, 211180, 401925, 766648, 1465899, 2808082, 5389509, 10360576, 19948155, 38460946, 74253513, 143527180, 277746975, 538048150, 1043342277, 2025049108

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

Sequence in context: A279100 A347415 A053992 * A003082 A058053 A264923

Adjacent sequences: A052822 A052823 A052824 * A052826 A052827 A052828

Keyword

easy,nonn

Author

encyclopedia(AT)pommard.inria.fr, Jan 25 2000

Extensions

More terms from Danny Rorabaugh, Oct 25 2015

Status

approved