

A255986


Decimal expansion of Sum_{m,n >= 1} (1)^(m + n)/(m*n*(m + n)).


0



3, 0, 0, 5, 1, 4, 2, 2, 5, 7, 8, 9, 8, 9, 8, 5, 7, 1, 3, 4, 9, 9, 3, 4, 5, 4, 0, 3, 7, 7, 8, 6, 2, 4, 9, 7, 6, 9, 1, 2, 4, 6, 5, 7, 3, 0, 8, 5, 1, 2, 4, 7, 2, 0, 4, 4, 8, 0, 6, 7, 8, 8, 8, 8, 3, 5, 4, 5, 9, 5, 5, 1, 4, 4, 6, 5, 7, 8, 2, 7, 2, 5, 4, 6, 6, 1, 3, 9, 6, 8, 4, 0, 2, 3, 3, 3, 8, 1, 4, 5, 3, 6, 5
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OFFSET

0,1


LINKS

Table of n, a(n) for n=0..102.
David H. Bailey and Jonathan M. Borwein, Computation and structure of character polylogarithms with applications to character MordellTornheimWitten sums, Mathematics of Computation, Vol. 85, No. 297 (2016), pp. 295324, alternative link.


FORMULA

Equals zeta(3)/4 = A002117/4.
From Amiram Eldar, Aug 07 2020: (Start)
Equals Integral_{x=0..oo} x^2/(exp(2*x)  1) dx.
Equals Integral_{x=0..1} x * log(x)^2/(1  x^2) dx. (End)


EXAMPLE

0.30051422578989857134993454037786249769124657308512472...


MAPLE

evalf(Zeta(3)/4, 120); # Vaclav Kotesovec, Mar 13 2015


MATHEMATICA

digits = 103; s = NSum[(1)^(m + n)/(m*n*(m + n)), {m, 1, Infinity}, {n, 1, Infinity}, WorkingPrecision > digits+10, Method > "AlternatingSigns"]; RealDigits[s, 10, digits] // First
RealDigits[Zeta[3]/4, 10, 100][[1]] (* Amiram Eldar, Aug 07 2020 *)


CROSSREFS

Cf. A002117.
Sequence in context: A210953 A254280 A092669 * A011400 A115013 A072736
Adjacent sequences: A255983 A255984 A255985 * A255987 A255988 A255989


KEYWORD

nonn,cons


AUTHOR

JeanFrançois Alcover, Mar 13 2015


STATUS

approved



