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A073017 Decimal expansion of the Product_{n>=1} (1 + 1/n^3).

%I A073017 #52 Nov 21 2024 10:36:31
%S A073017 2,4,2,8,1,8,9,7,9,2,0,9,8,8,7,0,3,2,8,7,3,6,0,4,1,4,3,6,1,7,9,1,4,6,
%T A073017 3,5,8,1,1,8,3,6,2,9,4,4,7,8,3,3,9,0,4,9,7,6,3,2,7,4,9,9,7,4,7,2,6,4,
%U A073017 4,4,7,3,4,1,2,0,8,6,8,3,6,8,1,2,3,8,0,5,5,0,1,5,7,2,0,5,9,0,4,3,8,8,1,3,8
%N A073017 Decimal expansion of the Product_{n>=1} (1 + 1/n^3).
%C A073017 Let X_1, X_2, ... be a sequence of independent Bernoulli trials with probability of success 1/n^3.  Let Y be the position of the last success in the sequence.  1.428189... is the expected value of Y. - _Geoffrey Critzer_, Aug 19 2019
%C A073017 If m tends to infinity, Product_{k>=1} (1 + m/k^3) ~ exp(2*Pi*m^(1/3)/sqrt(3)) / (2^(3/2)*Pi^(3/2)*sqrt(m)). - _Vaclav Kotesovec_, Aug 30 2024
%H A073017 Simon Plouffe, <a href="https://web.archive.org/web/20080205212854/http://www.worldwideschool.org/library/books/sci/math/MiscellaneousMathematicalConstants/chap78.html">product(1+1/n**3,n=1..infinity)</a>.
%H A073017 S. Ramanujan, <a href="http://www.imsc.res.in/~rao/ramanujan/NoteBooks/NoteBook2/chapterII/page9.htm">Notebook entry</a>.
%F A073017 Equals cosh(1/2 * sqrt(3) * Pi)/Pi.
%F A073017 Equals exp(Sum_{j>=1} (-(-1)^j*zeta(3*j)/j)). - _Vaclav Kotesovec_, Mar 28 2019
%F A073017 Equals Product_{n>=1} (1 + 1/(n^2 + n)). - _Amiram Eldar_, Sep 01 2020
%F A073017 Equals 3*Product_{n >= 2} (1-n^(-3)) = 3*A109219. - _Robert FERREOL_, Oct 06 2021
%e A073017 2.42818979209887032873604143617914635811836294478339049763...
%t A073017 RealDigits[ Cosh[Sqrt[3]*Pi/2]/Pi, 10, 105][[1]] (* _Jean-François Alcover_, Nov 18 2015 *)
%Y A073017 Cf. A000984, A006014, A109219, A175615, A175617, A156648, A258870, A258871, A334411.
%K A073017 cons,nonn
%O A073017 1,1
%A A073017 _Robert G. Wilson v_, Aug 03 2002