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A052821
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A simple grammar: pairs of cycles of sequences.
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1
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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
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OFFSET
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0,4
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LINKS
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FORMULA
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G.f.: (Sum_{j>=i} (A000010(j)/j)*log((x^j-1)/(2*x^j-1)))^2.
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MAPLE
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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
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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encyclopedia(AT)pommard.inria.fr, Jan 25 2000
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EXTENSIONS
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STATUS
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approved
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