A381655 Decimal expansion of the multiple zeta value (Euler sum) zetamult(5,1) = zetamult(3, 1, 1, 1).

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

Offset

0,2

Comments

For complete list of formulas of the positive multiple zeta values up to weight 6 see A381651.

Links

Table of n, a(n) for n=0..106.

Formula

zetamult(5,1) = Sum_{m>=2} (Sum_{n=1..m-1} 1/(m^5*n)) = 3*zeta(6)/4 - zeta(3)^2/2 = zetamult(3,1,1,1).

Example

0.04053689727151973782904590793969648...

Mathematica

RealDigits[3*Zeta[6]/4 - Zeta[3]^2/2, 10, 106][[1]]

Prog

(PARI) zetamult([3, 1, 1, 1])

Crossrefs

Cf. A381651, A381652, A381653, A381654, A381656, A381657.

Sequence in context: A185199 A201196 A377636 * A019906 A197251 A049247

Adjacent sequences: A381652 A381653 A381654 * A381656 A381657 A381658

Keyword

nonn,cons

Author

Artur Jasinski, Mar 11 2025

Status

approved