A384460 Decimal expansion of Sum_{k>=1} (-1)^(k+1)*H(k)^2/k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset

0,1

References

Ovidiu Furdui, Limits, Series, and Fractional Part Integrals, Springer, 2013, section 3.4, p. 148.

Links

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

Formula

Equals (9*zeta(3) + 4*log(2)^3 - Pi^2*log(2))/12.

Example

0.44246018937791249521879821917465633518413362702258...

Mathematica

RealDigits[(9*Zeta[3] + 4*Log[2]^3 - Pi^2*Log[2])/12, 10, 120][[1]]

Prog

(PARI) (9*zeta(3) + 4*log(2)^3 - Pi^2*log(2))/12

Crossrefs

Cf. A001008, A002805.

Cf. A000796, A002117, A002162.

Related constants: A152648, A152649, A152651, A218505, A233090, A238168, A238181, A238182, A241753, A244667, A253191, A256988, A345203.

Sequence in context: A193514 A112108 A373822 * A021230 A273278 A375850

Adjacent sequences: A384457 A384458 A384459 * A384461 A384462 A384463

Keyword

nonn,cons,easy

Author

Amiram Eldar, May 30 2025

Status

approved