A370000 Decimal expansion of Sum_{k>=0} (-1)^k/(3*k+2)^3.

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

Offset

0,3

Links

Table of n, a(n) for n=0..93.

R. W. Gosper, Acceleration of Series, Artificial Intelligence (1974) # 304.

Formula

Equals Sum_{n>=0} (-1)^n/A016791(n).

Equals A226735 - 13*zeta(3)/18 = 5*Pi^3/(2*3^(9/2)) - 13*zeta(3)/36.

Example

1/8 - 1/125 + 1/512 - 1/1331 + ... = 0.118438778425057529625616861943025438732887982...

Maple

5*Pi^3/2/3^(9/2)-13*Zeta(3)/36 ; evalf(%) ;

Mathematica

RealDigits[5*Pi^3/(2*3^(9/2)) - 13*Zeta[3]/36, 10, 120][[1]] (* Amiram Eldar, Feb 09 2024 *)

Prog

(PARI) sumalt(k=0, (-1)^k/(3*k+2)^3) \\ Michel Marcus, Feb 07 2024

Crossrefs

Cf. A226735, A016791.

Sequence in context: A091475 A197482 A292529 * A154211 A019723 A093822

Adjacent sequences: A369997 A369998 A369999 * A370001 A370002 A370003

Keyword

nonn,cons

Author

R. J. Mathar, Feb 07 2024

Status

approved