A384459 Decimal expansion of Sum_{k>=1} (-1)^k*(3*k+1)*H(k)^3/2^k, where H(k) = A001008(k)/A002805(k) is the k-th harmonic number.

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

Offset

0,2

References

K. Ramachandra and R. Sitaramachandrarao, On series, integrals and continued fractions - II, Madras Univ. J., Sect. B, 51 (1988), pp. 181-198.

Links

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

K. Ramachandra, On series integrals and continued fractions I, Hardy-Ramanujan Journal, Vol. 4 (1981), pp. 1-11.

K. Ramachandra, On series, integrals and continued fractions, III, Acta Arithmetica, Vol. 99, No. 3 (2001), pp. 257-266.

Michael Ian Shamos, Shamos's Catalog of the Real Numbers, 2011, p. 225.

Formula

Equals A016578^2 = log(3/2)^2 (Ramachandra, 1981).

Equals Sum_{k>=1} (-1)^(k+1)*H(k)/((k+1)*2^k), where H(k) = A001008(k)/A002805(k) is the k-th harmonic number (Shamos, 2011).

Example

0.16440195389316542965263621650302311406441305151904...

Mathematica

RealDigits[Log[3/2]^2, 10, 120][[1]]

Prog

(PARI) log(3/2)^2

Crossrefs

Cf. A001008, A002805, A016578.

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

Sequence in context: A082530 A099404 A095156 * A198550 A029680 A201285

Adjacent sequences: A384456 A384457 A384458 * A384460 A384461 A384462

Keyword

nonn,cons,easy

Author

Amiram Eldar, May 30 2025

Status

approved