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Decimal expansion of (1/4)^(4/9)^...^(n^2/(n+1)^2)^... .
4

%I #17 Mar 03 2021 06:04:44

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

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

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

%N Decimal expansion of (1/4)^(4/9)^...^(n^2/(n+1)^2)^... .

%e 0.4449047137975709943818158062572891757596036582203842557173...

%t digits = 120; difs = 1; sold = 0; n = 10; While[Abs[difs] > 10^(-digits - 5), s = N[n^2/(n + 1)^2, 1000]; Do[s = (m^2/(m + 1)^2)^s, {m, n - 1, 1, -1}]; difs = s - sold; sold = s; n++]; RealDigits[s, 10, 120][[1]] (* _Vaclav Kotesovec_, Feb 17 2021 *)

%Y Cf. A242759, A242760, A341325.

%K nonn,cons

%O 0,1

%A _Koksal Karakus_, Feb 08 2021

%E More digits from _Alois P. Heinz_, Feb 16 2021