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A241140 Decimal expansion of an infinite product involving the ratio of n! to its Stirling approximation. 2
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 (list; constant; graph; refs; listen; history; text; internal format)
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

Prod_{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: A099287 A058176 A155158 * A109986 A245741 A175473

Adjacent sequences:  A241137 A241138 A241139 * A241141 A241142 A241143

KEYWORD

nonn,cons,easy

AUTHOR

Jean-Fran├žois Alcover, Aug 08 2014

STATUS

approved

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Last modified July 11 00:56 EDT 2020. Contains 335600 sequences. (Running on oeis4.)