A144666 Decimal expansion of Product_{n=2..infinity} (n^7-1)/(n^7+1).

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

Offset

0,1

Links

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

J. Borwein et al., Experimentation in Mathematics, 2004, section 1.2.

Ryan Goulden, Closed-Form Evaluation of Arctanh Power Sums via Infinite Products, arXiv preprint arXiv:2602.06244 [math.GM], 2026.

E. W. Weisstein, Infinite Product, MathWorld.

Formula

Equals exp(-2*Sum_{k>=2} arctanh(1/k^7)). - Detlef Meya, Mar 25 2026

Example

0.9834397805869282351144875535540...

Mathematica

p = 2*Product[Gamma[2+(-1)^(k+k/7)], {k, 6}]/Product[Gamma[2-(-1)^(k+k/7)], {k, 6}]; RealDigits[Re[p], 10, 105][[1]] (* Jean-François Alcover, Feb 11 2013, updated Nov 18 2015 *)
RealDigits[Re[N[Product[(n^7 - 1)/(n^7 + 1), {n, 2, Infinity}], 110]]][[1]] (* Bruno Berselli, Apr 02 2013 *)

Crossrefs

Cf. A090986, A144664.

Sequence in context: A210649 A347331 A397874 * A255251 A363633 A224236

Adjacent sequences: A144663 A144664 A144665 * A144667 A144668 A144669

Keyword

nonn,cons

Author

R. J. Mathar, Feb 01 2009

Extensions

More terms from Jean-François Alcover, Feb 11 2013

Status

approved