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A181131
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Denominator of Integral_{x=0..+oo} Polylog(-n, -x)^2 for n > 0, with a(0) = 1.
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21
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1, 3, 15, 105, 105, 231, 15015, 2145, 36465, 969969, 4849845, 10140585, 10140585, 22287, 3231615, 7713865005, 7713865005, 90751353, 218257003965, 1641030105, 67282234305, 368217318651, 1841086593255, 3762220429695, 63957747304815, 1546231253523
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OFFSET
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0,2
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COMMENTS
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These are the denominators of the Bernoulli median numbers (see A212196). - Peter Luschny, May 04 2012
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LINKS
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FORMULA
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a(n) = denominator((-1)^n/Pi^(2*n)*integral((log(t/(1-t))*log(1-1/t))^n dt,t=0,1)). - [Gerry Martens, May 25 2011]
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MAPLE
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seq(denom(add(binomial(n, k)*bernoulli(n+k), k=0..n)), n=0..100); # Robert Israel, Jun 02 2015
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MATHEMATICA
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Table[Denominator[Integrate[PolyLog[-n, -x]^2, {x, 0, Infinity}]], {n, 1, 18}]
max = 25; t[0] = Table[BernoulliB[n], {n, 0, 2*max}]; t[n_] := Differences[t[0], n]; a[n_] := t[n][[n + 1]] // Denominator; Table[a[n], {n, 0, max}] (* Jean-François Alcover, Jul 25 2013, after Peter Luschny *)
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PROG
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(Sage) # uses[BernoulliMedian_list from A212196]
return [denominator(q) for q in BernoulliMedian_list(n)]
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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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EXTENSIONS
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Offset set to 0, a(0) and a(19)..a(25) added by Peter Luschny, May 04 2012
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STATUS
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approved
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