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A052825 A simple grammar. 2
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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: A212484 A279100 A053992 * A003082 A058053 A264923

Adjacent sequences:  A052822 A052823 A052824 * A052826 A052827 A052828

KEYWORD

easy,nonn,changed

AUTHOR

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

EXTENSIONS

More terms from Danny Rorabaugh, Oct 25 2015

STATUS

approved

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Last modified June 17 07:00 EDT 2019. Contains 324183 sequences. (Running on oeis4.)