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A058312
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Denominator of the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k.
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40
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1, 2, 6, 12, 60, 60, 420, 840, 2520, 2520, 27720, 27720, 360360, 360360, 72072, 144144, 2450448, 2450448, 46558512, 232792560, 232792560, 232792560, 5354228880, 5354228880, 26771144400, 26771144400, 80313433200, 11473347600
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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a(n) = the (reduced) denominator of the continued fraction 1/(1 + 1^2/(1 + 2^2/(1 + 3^2/(1 + ... + (n-1)^2/(1))))). - Peter Bala, Feb 18 2024
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EXAMPLE
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1, 1/2, 5/6, 7/12, 47/60, 37/60, 319/420, 533/840, 1879/2520, ...
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MAPLE
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A058313 := n->denom(add((-1)^(k+1)/k, k=1..n));
# Alternatively:
a := n -> denom(harmonic(n) - harmonic((n-modp(n, 2))/2)):
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MATHEMATICA
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a[n_] := Sum[(-1)^(k+1)/k, {k, 1, n}]; Table[a[n] // Denominator, {n, 1, 30}] (* Jean-François Alcover, May 26 2015 *)
a[n_]:= (-1)^n(HarmonicNumber[n/2-1/2]-HarmonicNumber[n/2]+(-1)^n Log[4])/2; Table[a[n] // FullSimplify, {n, 1, 29}] // Denominator (* Gerry Martens, Jul 05 2015 *)
Rest[Denominator[CoefficientList[Series[Log[1 + x]/(1 - x), {x, 0, 33}], x]]] (* Vincenzo Librandi, Jul 06 2015 *)
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PROG
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(PARI) a(n)=denominator(polcoeff(-log(1-x)/(x+1)+O(x^(n+1)), n))
(Haskell)
import Data.Ratio((%), denominator)
a058312 n = a058312_list !! (n-1)
a058312_list = map denominator $ scanl1 (+) $
map (1 %) $ tail a181983_list
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CROSSREFS
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Cf. A002805 (denominator of n-th harmonic number).
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KEYWORD
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nonn,frac,nice,easy
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AUTHOR
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STATUS
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approved
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