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 A242623 Decimal expansion of Product_{n>1} (1+1/n)^(1/n). 4

%I

%S 1,7,5,8,7,4,3,6,2,7,9,5,1,1,8,4,8,2,4,6,9,9,8,9,6,8,4,9,6,6,1,9,3,2,

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

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

%N Decimal expansion of Product_{n>1} (1+1/n)^(1/n).

%D S. R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 p. 122.

%H G. C. Greubel, <a href="/A242623/b242623.txt">Table of n, a(n) for n = 1..1000</a>

%F Equals exp(A131688)/2.

%e 1.758743627951184824699896849661932...

%p evalf(exp(sum((-1)^(n+1)*Zeta(n+1)/n, n=1..infinity))/2, 120); # _Vaclav Kotesovec_, Dec 11 2015

%t Exp[NSum[((-1)^n*(-1 + Zeta[n]))/(n - 1), {n, 2, Infinity}, NSumTerms -> 300, WorkingPrecision -> 105] ] // RealDigits[#, 10, 103]& // First

%o (PARI) default(realprecision, 100); exp(suminf(n=2, (-1)^n*(zeta(n)-1)/(n-1))) \\ _G. C. Greubel_, Nov 15 2018

%o (MAGMA) SetDefaultRealField(RealField(100)); L:=RiemannZeta(); Exp((&+[(-1)^n*(Evaluate(L,n)-1)/(n-1): n in [2..10^3]])); // _G. C. Greubel_, Nov 15 2018

%o (Sage) numerical_approx(exp(sum((-1)^k*(zeta(k)-1)/(k-1) for k in [2..1000])), digits=100) # _G. C. Greubel_, Nov 15 2018

%Y Cf. A131688, A242624, A244625.

%K nonn,cons

%O 1,2

%A _Jean-François Alcover_, May 19 2014

%E Data extended and Mma modified by _Jean-François Alcover_, May 23 2014

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Last modified August 22 05:00 EDT 2019. Contains 326172 sequences. (Running on oeis4.)