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

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, 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, 2, 1, 6, 1, 7, 5, 8, 0, 8, 3, 0, 7, 1, 7, 9, 7, 5

Offset: 1

Author

Jwalin Bhatt, Jul 06 2025

Keywords

• nonn
• cons

Comments

The geometric mean of the Poisson distribution with parameter value 1 (A385685) approaches this constant.

Examples

			1.4210379597319607153378144890592856953982...
		

Crossrefs

Cf. A296301, A306243, A382095, A385685.

Programs

Mathematica

N[Exp [Sum[Log[i]/Factorial[i], {i, 2, Infinity}] / (E-1) ], 120]

PARI

prodinf(k=2, k^(1/k!))^(1/(exp(1)-1))

Formula

Equals exp((Sum_{k>=2} log(k)/k!)/(e-1)).

Equals (Product_{k>=2} k^(1/k!)) ^ (1/(e-1)).

From Vaclav Kotesovec, Jul 08 2025: (Start)

Equals exp(A306243/(exp(1) - 1)).

Equals A296301^(1/(exp(1) - 1)). (End)