A397230 Decimal expansion of Sum_{k>=1} (-1)^(k+1) * AH(2*k,2)/k, where AH(k,2) = A119682(k)/A334580(k) is the k-th alternating harmonic (or skew-harmonic) number of order 2.

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Cornel Ioan Vălean, More (Almost) Impossible Integrals, Sums, and Series, Springer Cham, 2023. See section 4.22, p. 426.

Index entries for sequences related to harmonic numbers.

Formula

Equals 3*zeta(3)/2 + log(2)*zeta(2)/8 - Pi*G/2, where G is Catalan's constant (A006752).

Example

0.5068126402656674468951396413804447542421309686549903...

Mathematica

RealDigits[3*Zeta[3]/2 + Log[2]*Zeta[2]/8 - Pi*Catalan/2, 10, 120][[1]]

Prog

(PARI) 3*zeta(3)/2 + log(2)*zeta(2)/8 - Pi*Catalan/2

Crossrefs

Cf. A119682, A334580.

Cf. A002117, A002162, A013661, A006752.

Sum_{k>=1} (-1)^(k+1) * AH(2*k, m)/k: A397229 (m=1), this constant (m=2), A397231 (m=3), A397232 (m=4).

Sequence in context: A320375 A361918 A200419 * A271522 A343015 A069206

Adjacent sequences: A397227 A397228 A397229 * A397231 A397232 A397233

Keyword

nonn,cons,new

Author

Amiram Eldar, Jun 19 2026

Status

approved