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

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, 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, 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

Offset

0,1

Links

Table of n, a(n) for n=0..102.

Eric Weisstein's MathWorld, Multivariate Zeta Function

Wikipedia, Multiple zeta function

Formula

zetamult(2,4) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^2*n^4)) = (25/12)*zeta(6) - zeta(3)^2.

Equals Sum_{i, j >= 1} 1/(i^4*j^2*binomial(i+j, i)). - Peter Bala, Aug 05 2025

Example

0.67452391403396814049156060825742993927838436513788957970691722144377...

Mathematica

RealDigits[(25/12)*Zeta[6] - Zeta[3]^2, 10, 103] // First

Prog

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

Crossrefs

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).

Sequence in context: A395807 A019932 A004447 * A005351 A098882 A254374

Adjacent sequences: A258986 A258987 A258988 * A258990 A258991 A258992

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Jun 16 2015

Status

approved