A355500 Decimal expansion of Product_{k>=1} (k - 1/2)^(1/(k - 1/2)) / k^(1/k).

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

Offset

0,1

Links

Table of n, a(n) for n=0..105.

Formula

Equals 1 / 2^(2*gamma + log(2)), where gamma is the Euler-Mascheroni constant A001620.

Example

0.277858347832723878490708523330309732997337264470326508064631180586776...

Maple

evalf(1 / 2^(2*gamma + log(2)), 120);

Mathematica

RealDigits[1 / 2^(2*EulerGamma + Log[2]), 10, 120][[1]]

Prog

(PARI) default(realprecision, 200); exp(sumpos(n=1, log(n - 1/2)/(n - 1/2) - log(n)/n))

Crossrefs

Cf. A001620, A115522, A355499.

Sequence in context: A246553 A330479 A349804 * A257960 A238734 A332633

Adjacent sequences: A355497 A355498 A355499 * A355501 A355502 A355503

Keyword

nonn,cons

Author

Vaclav Kotesovec, Jul 04 2022

Status

approved