A397226 - OEIS

A397226

Decimal expansion of Sum_{k>=1} (-1)^(k+1) * AH(k)/k^4, where AH(k) = A058313(k)/A058312(k) is the k-th alternating harmonic (or skew-harmonic) number.

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

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OFFSET

0,1

LINKS

Table of n, a(n) for n=0..104.

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2nd ed., 2023, section 4.1, p. 261.

Cornel Ioan Vălean, More (Almost) Impossible Integrals, Sums, and Series, Springer Cham, 2023. See section 4.22, p. 427.

Index entries for sequences related to harmonic numbers.

FORMULA

Equals 15*log(2)*zeta(4)/8 + 3*zeta(2)*zeta(3)/4 - 59*zeta(5)/32.

EXAMPLE

0.977785147742505393279597210624915283756731530936315...