A397289 - OEIS

A397289

Decimal expansion of Sum_{k>=1} (-1)^(k+1) * AH(k,4)/k, where AH(k,4) = A120296(k)/A334585(k) is the k-th alternating harmonic (or skew-harmonic) number of order 4.

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

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OFFSET

0,1

LINKS

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

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 91*zeta(5)/32 - 3*zeta(2)*zeta(3)/4 - log(2)*zeta(4).

EXAMPLE

0.715575743064587949327546123576358548590517797492934...

MATHEMATICA