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A195189
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Denominators of a sequence leading to gamma = A001620.
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14
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2, 24, 72, 2880, 800, 362880, 169344, 29030400, 9331200, 4790016000, 8673280, 31384184832000, 6181733376000, 439378587648000, 10346434560000, 512189896458240000, 265423814656, 14148260909088768000, 2076423318208512000, 96342919523794944000000, 74538995631567667200000
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OFFSET
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0,1
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COMMENTS
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gamma = 1/2 + 1/24 + 1/72 + 19/2880 + 3/800 + 863/362880 + 275/169344 + ... = (A002206 unsigned=reduced A141417(n+1)/A091137(n+1))/a(n) is an old formula based on Gregory's A002206/A002207.
This formula for Euler's constant was discovered circa 1780-1790 by the Italian mathematicians Gregorio Fontana (1735-1803) and Lorenzo Mascheroni (1750-1800), and was subsequently rediscovered several times (in particular, by Ernst Schröder in 1879, Niels E. Nørlund in 1923, Jan C. Kluyver in 1924, Charles Jordan in 1929, Kenter in 1999, and Victor Kowalenko in 2008). For more details, see references below. - Iaroslav V. Blagouchine, May 03 2015
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LINKS
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FORMULA
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EXAMPLE
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a(0)=1*2, a(1)=2*12, a(2)=3*24, a(3)=4*720.
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MATHEMATICA
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g[n_]:=Sum[StirlingS1[n, l]/(l+1), {l, 1, n}]/(n*n!); a[n_]:=Denominator[g[n]]; Table[a[n], {n, 1, 30}] (* Iaroslav V. Blagouchine, May 03 2015 *)
g[n_] := Sum[ BernoulliB[j]/j * StirlingS1[n, j-1], {j, 1, n+1}] / n! ; a[n_] := (n+1)*Denominator[g[n]]; Table[a[n], {n, 0, 20}]
(* or *) max = 20; Denominator[ CoefficientList[ Series[ 1/Log[1 + x] - 1/x, {x, 0, max}], x]]*Range[max+1] (* Jean-François Alcover, Sep 04 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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