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A258989 Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,4).

%I A258989 #16 Aug 08 2025 00:47:45
%S A258989 6,7,4,5,2,3,9,1,4,0,3,3,9,6,8,1,4,0,4,9,1,5,6,0,6,0,8,2,5,7,4,2,9,9,
%T A258989 3,9,2,7,8,3,8,4,3,6,5,1,3,7,8,8,9,5,7,9,7,0,6,9,1,7,2,2,1,4,4,3,7,7,
%U A258989 4,8,5,8,2,4,7,7,2,4,8,5,1,9,5,6,2,5,2,6,8,8,8,5,3,4,3,0,7,9,1,2,7,8,1
%N A258989 Decimal expansion of the multiple zeta value (Euler sum) zetamult(2,4).
%H A258989 Eric Weisstein's MathWorld, <a href="https://mathworld.wolfram.com/MultivariateZetaFunction.html">Multivariate Zeta Function</a>
%H A258989 Wikipedia, <a href="https://en.wikipedia.org/wiki/Multiple_zeta_function">Multiple zeta function</a>
%F A258989 zetamult(2,4) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^2*n^4)) = (25/12)*zeta(6) - zeta(3)^2.
%F A258989 Equals Sum_{i, j >= 1} 1/(i^4*j^2*binomial(i+j, i)). - _Peter Bala_, Aug 05 2025
%e A258989 0.67452391403396814049156060825742993927838436513788957970691722144377...
%t A258989 RealDigits[(25/12)*Zeta[6] - Zeta[3]^2, 10, 103] // First
%o A258989 (PARI) zetamult([2,4]) \\ _Charles R Greathouse IV_, Jan 21 2016
%Y A258989 Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258984 (4,2), A258985 (5,2), A258947 (6,2), A258986 (2,3), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258990 (3,4), A258991 (4,4).
%K A258989 nonn,cons,easy
%O A258989 0,1
%A A258989 _Jean-François Alcover_, Jun 16 2015