A258984 Decimal expansion of the multiple zeta value (Euler sum) zetamult(4,2).

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

Offset

0,2

Links

Table of n, a(n) for n=0..107.

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(4,2) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^4*n^2)) = zeta(3)^2 - (4/3)*zeta(6).

Equals zeta(2)*zeta(4) - zeta(6) - Sum_{i, j >= 1} 1/(i^4*j^2*binomial(i+j, j)). - Peter Bala, Oct 18 2025

Example

0.088483382454368714294327839085760456647978752386750591674889276559474...

Mathematica

Join[{0}, RealDigits[Zeta[3]^2 - (4/3)*Zeta[6], 10, 107] // First]

Prog

(PARI) zetamult([4, 2]) \\ Charles R Greathouse IV, Jan 21 2016

Crossrefs

Cf. A072691 (zetamult(1,1)), A197110 (zetamult(2,2)), A258983 (zetamult(3,2)), A258985 (5,2), A258947 (6,2), A258986 (2,3), A258987 (3,3), A258988 (4,3), A258982 (5,3), A258989 (2,4), A258990 (3,4), A258991 (4,4).

Sequence in context: A388453 A388521 A154841 * A112116 A394600 A228719

Adjacent sequences: A258981 A258982 A258983 * A258985 A258986 A258987

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved