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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
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
Sequence in context: A058176 A155158 A344111 * A109986 A245741 A175473
KEYWORD
nonn,cons,easy
AUTHOR
STATUS
approved

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Last modified April 15 20:47 EDT 2024. Contains 371696 sequences. (Running on oeis4.)