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%I #13 Jan 21 2016 14:43:21
%S 0,1,7,8,1,9,7,4,0,4,1,6,8,3,5,9,8,8,3,6,2,6,5,9,5,3,0,2,4,8,7,2,4,6,
%T 1,2,1,6,8,7,1,3,1,3,7,1,1,0,2,9,1,1,8,8,4,1,8,8,2,1,3,6,1,9,1,7,6,1,
%U 3,4,8,0,2,7,6,4,1,6,0,4,6,3,7,1,8,2,8,6,2,1,0,1,9,2,0,5,8,7,9,4
%N Decimal expansion of the multiple zeta value (Euler sum) zetamult(6,2).
%H Eric Weisstein's MathWorld, <a href="http://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiple_zeta_function">Multiple zeta function</a>
%F zetamult(6,2) = Sum_{m>=2} (sum_{n=1..m-1} 1/(m^6*n^2)).
%F Equals Sum_{m>=2} H(m-1, 2)/m^6, where H(n,2) is the n-th harmonic number of order 2.
%e 0.01781974041683598836265953024872461216871313711029118841882136191761348...
%t digits = 99; zetamult[6,2] = NSum[HarmonicNumber[m-1, 2]/m^6, {m, 2, Infinity}, WorkingPrecision -> digits+20, NSumTerms -> 200, Method -> {"NIntegrate", "MaxRecursion" -> 18}]; Join[{0}, RealDigits[zetamult[6,2], 10, digits] // First]
%o (PARI) zetamult([6,2]) \\ _Charles R Greathouse IV_, Jan 21 2016
%Y Cf. A072691, A197110.
%K nonn,cons
%O 0,3
%A _Jean-François Alcover_, Jun 15 2015
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