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%I #27 May 14 2020 11:17:54
%S 1,1,5,6,3,6,2,6,8,4,3,3,2,2,6,9,7,1,6,8,5,3,3,7,0,3,2,2,8,8,7,3,6,9,
%T 3,5,6,5,1,3,0,1,4,5,4,3,8,9,1,8,8,8,6,3,7,9,9,9,2,5,9,5,9,8,9,8,3,1,
%U 7,7,8,1,6,0,7,2,8,2,6,1,9,4,6,0,7,9,0,8,1,3,3,8,2,0,3,7,8,3,1,7
%N Decimal expansion of (1*(2*(3*...)^(1/3))^(1/3))^(1/3).
%C Cubic recurrence constant (see A123851): a cubic analog of Somos's quadratic recurrence constant A112302.
%D S. R. Finch, Mathematical Constants, Cambridge University Press, Cambridge, 2003, p. 446.
%H Kh. Hessami Pilehrood and T. Hessami Pilehrood, <a href="https://arxiv.org/abs/0808.0410">Vacca-type series for values of the generalized-Euler-constant function and its derivative</a>, arXiv:0808.0410 [math.NT], 2008.
%H Kh. Hessami Pilehrood and T. Hessami Pilehrood, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL13/Pilehrood/pilehrood2.html">Vacca-type series for values of the generalized-Euler-constant function and its derivative</a>, Journal of Integer Sequences 13 (2010), Article 10.7.3.
%H Jonathan Sondow and Petros Hadjicostas, <a href="https://arxiv.org/abs/math/0610499">The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant</a>, arXiv:math/0610499 [math.CA], 2006.
%H Jonathan Sondow and Petros Hadjicostas, <a href="http://dx.doi.org/10.1016/j.jmaa.2006.09.081">The generalized-Euler-constant function gamma(z) and a generalization of Somos's quadratic recurrence constant</a>, J. Math. Anal. Appl. 332(1) (2007), 292-314.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SomossQuadraticRecurrenceConstant.html">Somos's Quadratic Recurrence Constant</a>.
%F Product_{n>=1} n^(1/3^n).
%e 1.156362684332269716853370322887369356513014543891888637999259598983177816...
%t Take[RealDigits[Product[N[n^3^-n,200], {n,400}]][[1]], 100].
%t RealDigits[Exp[-D[PolyLog[n, 1/3], n]/.n->0], 10, 100][[1]] (* _Jean-François Alcover_, Jan 28 2014 *)
%o (PARI) prodinf(n=1, n^(1/3^n)) \\ _Michel Marcus_, Aug 03 2019
%Y Cf. A052129, A112302, A116603, A123851, A123853, A123854.
%K cons,easy,nonn
%O 1,3
%A _Petros Hadjicostas_ and _Jonathan Sondow_, Oct 15 2006
%E References updated by _R. J. Mathar_, Aug 12 2010
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