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 A181130 Numerator of Integral_{x=0..+oo} Polylog(-n, -x)^2. 5
 1, 2, 8, 8, 32, 6112, 3712, 362624, 71706112, 3341113856, 79665268736, 1090547664896, 38770843648, 106053090598912, 5507347586961932288, 136847762542978039808, 45309996254420664320, 3447910579774800362340352 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS (-1)^n*a(n) is the numerator on the main diagonal of the (truncated) array described in A168516. - Paul Curtz, Jun 20 2011 These are - up to signs - the numerators of the Bernoulli median numbers (see A212196). - Peter Luschny, May 04 2012 LINKS Peter Luschny, The computation and asymptotics of the Bernoulli numbers. FORMULA a(n) = numerator((-1)^n/Pi^(2*n)*integral((log(t/(1-t))*log(1-1/t))^n dt,t=0,1)). - [Gerry Martens, May 25 2011] MAPLE seq(numer((-1)^n*add(binomial(n, k)*bernoulli(n+k), k=0..n)), n=1..30); # Robert Israel, Jun 02 2015 MATHEMATICA Table[Numerator[Integrate[PolyLog[-n, -x]^2, {x, 0, Infinity}]], {n, 1, 18}] PROG (Sage) # uses[BernoulliMedian_list from A212196] def A181130_list(n): return [q.numerator() for q in BernoulliMedian_list(n)] # Peter Luschny, May 04 2012 (PARI) a(n)=(-1)^n*sum(k=0, n, binomial(n, k)*bernfrac(n+k)) \\ Charles R Greathouse IV, Jun 03 2015 CROSSREFS Cf. A181131 (denominator), A212196. Sequence in context: A227326 A323852 A064231 * A212196 A156052 A170923 Adjacent sequences: A181127 A181128 A181129 * A181131 A181132 A181133 KEYWORD nonn,frac AUTHOR Vladimir Reshetnikov, Jan 23 2011 STATUS approved

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Last modified March 27 13:28 EDT 2023. Contains 361572 sequences. (Running on oeis4.)