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
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
KEYWORD
nonn,frac
AUTHOR
Vladimir Reshetnikov, Jan 23 2011
STATUS
approved