login
A simple grammar: pairs of cycles of sequences.
1

%I #27 Apr 18 2017 10:32:30

%S 0,0,1,4,10,22,43,84,157,294,551,1032,1941,3666,6955,13224,25269,

%T 48362,92875,178640,344453,665130,1286699,2492184,4834061,9386650,

%U 18247971,35508348,69161705,134822934,263039047,513566944,1003425345,1961815578,3838001099

%N A simple grammar: pairs of cycles of sequences.

%H Danny Rorabaugh, <a href="/A052821/b052821.txt">Table of n, a(n) for n = 0..1000</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=786">Encyclopedia of Combinatorial Structures 786</a>

%F G.f.: (Sum_{j>=i} (A000010(j)/j)*log((x^j-1)/(2*x^j-1)))^2.

%p pairs spec := [S,{B=Sequence(Z,1 <= card),C=Cycle(B),S=Prod(C,C)},unlabeled]: seq(combstruct[count](spec,size=n), n=0..20);

%p h := n -> add(numtheory: phi(j)/j*log((x^j-1)/(2*x^j-1)), j=1..n): seq(coeff(series(h(n)^2, x, n+1), x, n), n=0..34); # _Danny Rorabaugh_, Oct 25 2015

%o (Sage) var('x'); a = lambda n: expand(sum([taylor(euler_phi(i)/i * log((x^i - 1)/(2*x^i - 1)),x,0,n) for i in range(1,n+1)])^2).coefficient(x^n) # _Danny Rorabaugh_, Oct 25 2015

%K nonn,easy

%O 0,4

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

%E More terms from _Danny Rorabaugh_, Oct 25 2015