A052821 A simple grammar: pairs of cycles of sequences.

0, 0, 1, 4, 10, 22, 43, 84, 157, 294, 551, 1032, 1941, 3666, 6955, 13224, 25269, 48362, 92875, 178640, 344453, 665130, 1286699, 2492184, 4834061, 9386650, 18247971, 35508348, 69161705, 134822934, 263039047, 513566944, 1003425345, 1961815578, 3838001099

Offset

0,4

Links

Danny Rorabaugh, Table of n, a(n) for n = 0..1000

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 786

Formula

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

Maple

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);
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

Prog

(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

Crossrefs

Sequence in context: A023626 A048574 A052837 * A292445 A023628 A294683

Adjacent sequences: A052818 A052819 A052820 * A052822 A052823 A052824

Keyword

nonn,easy

Author

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

Extensions

More terms from Danny Rorabaugh, Oct 25 2015

Status

approved