A241140 Decimal expansion of an infinite product involving the ratio of n! to its Stirling approximation.

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

Offset

1,3

Comments

The same product where the ratio is replaced by sqrt(2*Pi) evaluates as (2*Pi)^(1/4) = 1.58323...

References

Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 2.15 Glaisher-Kinkelin Constant, p. 135.

Links

Table of n, a(n) for n=1..101.

Steven R. Finch, Errata and Addenda to Mathematical Constants, p. 20.

Eric Weisstein's MathWorld, Glaisher-Kinkelin Constant

Formula

Product_{n>=1} (n! / ((sqrt(2*Pi*n)*n^n)/e^n))^((-1)^(n-1)) = A^3/(2^(7/12)*Pi^(1/4)), where A is the Glaisher-Kinkelin constant.

Example

1.057328141001876924952657094184286643131791252628433822095146...

Mathematica

RealDigits[Glaisher^3/(2^(7/12)*Pi^(1/4)), 10, 101] // First

Crossrefs

Cf. A019727, A074962.

Sequence in context: A058176 A155158 A344111 * A109986 A245741 A175473

Adjacent sequences: A241137 A241138 A241139 * A241141 A241142 A241143

Keyword

nonn,cons,easy

Author

Jean-François Alcover, Aug 08 2014

Status

approved