A144664 Decimal expansion of Product_{n>=2} (n^5-1)/(n^5+1).

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

Offset

0,1

Links

Table of n, a(n) for n=0..109.

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.

Eric Weisstein's World of Mathematics, Infinite Product.

Formula

Equals exp(-2*Sum_{k>=2} arctanh(1/k^5)). - Detlef Meya, Mar 23 2026

Example

0.92878693579955245375146991...

Maple

evalf[120](exp(-2*sum(arctanh(1/k^5), k=2..infinity)));  # Alois P. Heinz, Mar 23 2026

Mathematica

p = 2*Gamma[2-(-1)^(1/5)] * Gamma[2+(-1)^(2/5)] * Gamma[2-(-1)^(3/5)] * Gamma[2+(-1)^(4/5)] / (Gamma[2+(-1)^(1/5)] * Gamma[2-(-1)^(2/5)] * Gamma[2+(-1)^(3/5)] * Gamma[2-(-1)^(4/5)]); RealDigits[Re[p], 10, 110][[1]] (* Jean-François Alcover, Feb 11 2013, updated Nov 18 2015 *)
RealDigits[Re[N[Product[(n^5 - 1)/(n^5 + 1), {n, 2, Infinity}], 110]]][[1]] (* Bruno Berselli, Apr 02 2013 *)
RealDigits[Exp[-2 NSum[ArcTanh[1/k^5], {k, 2, Infinity}, WorkingPrecision -> 120, NSumTerms -> 200, Method -> {"NIntegrate", "MaxRecursion" -> 18}]], 10, 110][[1]] (* Detlef Meya, Mar 23 2026 *)

Crossrefs

Cf. A090986, A255435.

Sequence in context: A011453 A125580 A086238 * A241560 A309821 A073007

Adjacent sequences: A144661 A144662 A144663 * A144665 A144666 A144667

Keyword

nonn,cons

Author

R. J. Mathar, Feb 01 2009

Extensions

More terms from Jean-François Alcover, Feb 11 2013

Status

approved