A397025 Decimal expansion of Sum_{k>=0} binomial(2*k, k)^2 * (H(2*k) - H(k) - log(2))^2 / 16^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

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 4.4, "A Great Time with a Special Binoharmonic Series", p. 396, eq.(4.15), section 5.4, p. 457, and section 6.4, pp. 489-490.

Index entries for sequences related to harmonic numbers.

Formula

Equals 2*G - 7*zeta(3)/(2*Pi), where G is Catalan's constant (A006752).

Example

0.49273810224534183223367103902173674195735569863671...

Mathematica

RealDigits[2*Catalan - 7*Zeta[3]/(2*Pi), 10, 120][[1]]

Prog

(PARI) 2*Catalan - 7*zeta(3)/(2*Pi)

Crossrefs

Cf. A000984, A001008, A002805, A002894.

Cf. A002117, A002162, A006752, A221209.

Sequence in context: A388335 A021207 A200094 * A277526 A196505 A382603

Adjacent sequences: A397022 A397023 A397024 * A397026 A397027 A397028

Keyword

nonn,cons

Author

Amiram Eldar, Jun 14 2026

Status

approved