A398123 Decimal expansion of Sum_{k>=1} (-1)^(k+1) * H(2*k)/k^2, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset

1,3

Links

Table of n, a(n) for n=1..105.

Ali Shadhar Olaikhan, An Introduction to the Harmonic Series and Logarithmic Integrals, 2nd ed., 2023, section 4.3.3, pp. 306-307, eq. (4.80).

Index entries for sequences related to harmonic numbers.

Formula

Equals Pi*G - 23*zeta(3)/16, where G is Catalan's constant (A006752).

Example

1.149633983316244366515456559348838438390186604813211...

Mathematica

RealDigits[Pi*Catalan - 23*Zeta[3]/16, 10, 120][[1]]

Prog

(PARI) Pi*Catalan - 23*zeta(3)/16

Crossrefs

Cf. A001008, A002805.

Cf. A002117, A006752, A393257.

Sequence in context: A338142 A245299 A201415 * A395849 A363939 A094090

Adjacent sequences: A398120 A398121 A398122 * A398124 A398125 A398126

Keyword

nonn,cons,new

Author

Amiram Eldar, Jul 21 2026

Status

approved