A386009 Decimal expansion of Product_{k>=2} k^( ((k/2)^(k-1)) / (exp(k/2)*k!) ).

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

Offset: 1

Author

Jwalin Bhatt, Jul 14 2025

Keywords

• nonn
• cons

Comments

The geometric mean of the Borel distribution with parameter value 1/2 (A386016) approaches this constant. In general, for parameter value p it approaches Product_{k>=2} k^(((p*k)^(k-1))/((e^(p*k))*k!)).

Examples

			1.549251043425634048400544028158943555...
		

Crossrefs

Cf. A386016.

Programs

Mathematica

Exp[NSum[((k/2)^(k-1) * Log[k])/(E^(k/2) * Factorial[k]), {k, 2, Infinity}, WorkingPrecision -> 120, NSumTerms -> 1000]]

Formula

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