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A276593
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Denominator of the rational part of the sum of reciprocals of even powers of odd numbers, i.e., Sum_{k>=1} 1/(2*k-1)^(2*n).
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4
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8, 96, 960, 161280, 2903040, 638668800, 49816166400, 83691159552000, 2845499424768000, 1946321606541312000, 408727537373675520000, 48662619743783485440000, 124089680346647887872000000, 174221911206693634572288000000, 70734095949917615636348928000000
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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A276592(n)/a(n) = (-1)^(n+1) * B_{2*n} * (2^(2*n) - 1) / (2 * (2*n)!), where B_n is the Bernoulli number. - Seiichi Manyama, Sep 03 2018
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EXAMPLE
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--+---------------+------------------------------------
1 | 9.8... | 8
2 | 97.4... | 96
3 | 961.3... | 960
4 | 9488.5... | 161280/17 = 9487.0...
5 | 93648.0... | 2903040/31 = 93646.4...
6 | 924269.1... | 638668800/691 = 924267.4...
7 | 9122171.1... | 49816166400/5461 = 9122169.2... (End)
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MAPLE
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seq(denom(sum(1/(2*k-1)^(2*n), k=1..infinity)/Pi^(2*n)), n=1..22);
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MATHEMATICA
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a[n_]:=Denominator[1/2 SeriesCoefficient[1/(E^x+1), {x, 0, 2 n-1}]] (* Steven Foster Clark, Mar 10 2023 *)
a[n_]:=Denominator[1/2 Residue[Zeta[s] Gamma[s] (1-2^(1-s)) x^(-s), {s, 1-2 n}]] (* Steven Foster Clark, Mar 11 2023 *)
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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