A244625 - OEIS

%I #22 Sep 08 2022 08:46:08

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

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

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

%N Decimal expansion of Product_{n>1} (1 - 1/n^2)^(1/n).

%D Steven R. Finch, Mathematical Constants, Cambridge, 2003, Section 2.9 Alladi-Grinstead Constant, p. 122.

%H G. C. Greubel, <a href="/A244625/b244625.txt">Table of n, a(n) for n = 0..1000</a>

%F Equals exp(-Sum_{n>0} (zeta(2*n+1) - 1)/n).

%F Equals A242623 * A242624.

%F Also equals A242623 * exp(-A085361).

%e 0.7993704013063328789872528539753525668777...

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

%t digits = 102; Exp[-NSum[(Zeta[2*n+1]-1)/n, {n, 1, Infinity}, NSumTerms -> 300, WorkingPrecision -> digits+10]] // RealDigits[#, 10, digits]& // First

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

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

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

%Y Cf. A085361, A242623, A242624.

%K nonn,cons

%O 0,1

%A _Jean-François Alcover_, Jul 02 2014