cp's OEIS Frontend

A385686 Decimal expansion of exp((Sum_{k>=2} log(k)/k!)/(e-1)).

%I A385686 #21 Aug 13 2025 00:52:17
%S A385686 1,4,2,1,0,3,7,9,5,9,7,3,1,9,6,0,7,1,5,3,3,7,8,1,4,4,8,9,0,5,9,2,8,5,
%T A385686 6,9,5,3,9,8,2,5,7,1,7,4,2,9,3,2,0,0,7,8,6,8,1,0,2,8,0,5,1,8,1,5,8,2,
%U A385686 2,1,6,1,7,5,8,0,8,3,0,7,1,7,9,7,5
%N A385686 Decimal expansion of exp((Sum_{k>=2} log(k)/k!)/(e-1)).
%C A385686 The geometric mean of the Poisson distribution with parameter value 1 (A385685) approaches this constant.
%F A385686 Equals exp((Sum_{k>=2} log(k)/k!)/(e-1)).
%F A385686 Equals (Product_{k>=2} k^(1/k!)) ^ (1/(e-1)).
%F A385686 From _Vaclav Kotesovec_, Jul 08 2025: (Start)
%F A385686 Equals exp(A306243/(exp(1) - 1)).
%F A385686 Equals A296301^(1/(exp(1) - 1)). (End)
%e A385686 1.4210379597319607153378144890592856953982...
%t A385686 N[Exp [Sum[Log[i]/Factorial[i], {i, 2, Infinity}] / (E-1) ], 120]
%o A385686 (PARI) prodinf(k=2, k^(1/k!))^(1/(exp(1)-1))
%Y A385686 Cf. A296301, A306243, A382095, A385685.
%K A385686 nonn,cons
%O A385686 1,2
%A A385686 _Jwalin Bhatt_, Jul 06 2025