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%I #24 Sep 08 2022 08:46:23
%S 4,0,2,5,9,2,6,3,6,3,2,2,4,7,8,2,4,7,5,7,4,4,6,7,2,1,5,8,4,3,9,9,0,1,
%T 6,4,3,7,4,6,4,1,4,8,2,4,4,4,4,0,9,3,7,3,9,5,1,6,8,4,2,3,1,9,1,4,1,8,
%U 5,3,0,3,1,2,6,8,8,5,3,3,7,1,4,6,7,6,5
%N Decimal expansion of exp(-9 + 5*phi), where phi is the golden ratio.
%H Muniru A Asiru, <a href="/A322259/b322259.txt">Table of n, a(n) for n = 0..2000</a>
%H Don Redmond, <a href="https://www.fq.math.ca/Scanned/32-3/redmond.pdf">Infinite products and Fibonacci numbers</a>, Fib. Quart., Vol. 32, No. 3 (1994), pp. 234-239.
%F Equals Product_{k>=1} (L(k)/(sqrt(5)*F(k)))^(mu(k)/k), where L(k) and F(k) are the Lucas and Fibonacci numbers, and mu(k) is the Moebius function.
%F Equals exp(-A226765).
%e 0.40259263632247824757446721584399016437464148244440...
%p evalf[100](exp(-9+5*(1+sqrt(5))/2)); # _Muniru A Asiru_, Dec 06 2018
%t RealDigits[Exp[-9+5*GoldenRatio], 10, 120][[1]]
%o (PARI) exp(-(13-5*sqrt(5))/2) \\ _Michel Marcus_, Dec 02 2018
%o (Magma) SetDefaultRealField(RealField(100)); Exp(-(13-5*Sqrt(5))/2); // _G. C. Greubel_, Dec 16 2018
%o (Sage) numerical_approx(exp(-(9-5*golden_ratio)), digits=100) # _G. C. Greubel_, Dec 16 2018
%Y Cf. A000032, A000045, A001622, A008683, A226765, A322258.
%K nonn,cons
%O 0,1
%A _Amiram Eldar_, Dec 01 2018
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