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A250401
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Denominator of the harmonic mean of the first n nonzero octagonal numbers.
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3
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1, 9, 197, 503, 6623, 17813, 340527, 3763087, 169947523, 170436583, 5295982873, 90208585541, 3343268872217, 3348036962687, 144143598106421, 1659445372263179, 11627213232841853, 3879029288899801, 352907045903771, 10241306344308349, 208368821623076563
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OFFSET
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1,2
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COMMENTS
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a(n+1), for n >= 0, is also the numerator of the partial sums of the reciprocal octagonal numbers Sum_{k=0..n} 1/((k + 1)*(3*k + 1)) with the denominators given in A294512(n) [assuming that n+1 divides A250400(n+1) to give A294512(n) for n >= 0]. - Wolfdieter Lang, Nov 01 2017
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LINKS
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FORMULA
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Denominator of 12*n/(Pi*sqrt(3) + 9*log(3) + 6*Psi(n+1/3) - 6*Psi(n+1)). - Robert Israel, Nov 01 2017
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EXAMPLE
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a(3) = 197 because the octagonal numbers A000567(n), for n = 1..3, are [1,8,21], and 3/(1/1 + 1/8 + 1/21) = 504/197.
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MAPLE
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f:= n -> denom(n/add(1/(k*(3*k-2)), k=1..n)):
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MATHEMATICA
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With[{s = Array[PolygonalNumber[8, #] &, 21]}, Denominator@ Array[HarmonicMean@ Take[s, #] &, Length@ s]] (* Michael De Vlieger, Nov 01 2017 *)
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PROG
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(PARI)
harmonicmean(v) = #v / sum(k=1, #v, 1/v[k])
s=vector(30); for(n=1, #s, s[n]=denominator(harmonicmean(vector(n, k, 3*k^2-2*k)))); s
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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