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A100072 Decimal expansion of Product_{n>=1} (1/e * (1/(3*n)+1)^(3*n+1/2)). 0
1, 0, 1, 2, 3, 7, 8, 5, 5, 2, 7, 2, 2, 9, 1, 2, 2, 4, 9, 5, 3, 9, 6, 0, 2, 9, 6, 0, 4, 9, 6, 6, 8, 8, 6, 9, 2, 9, 7, 8, 0, 4, 4, 8, 7, 5, 8, 6, 9, 1, 7, 7, 1, 5, 0, 2, 8, 2, 0, 2, 2, 6, 5, 9, 5, 9, 2, 9, 3, 5, 4, 3, 2, 4, 3, 1, 0, 7, 8, 0, 9, 2, 3, 4, 6, 6, 1, 5, 9, 2, 9, 7, 4, 0, 3, 1, 1, 5, 8, 6, 8, 2 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..101.

Eric Weisstein's World of Mathematics, Infinite Product

FORMULA

3^(13/24) * exp(1 + (2*Pi^2 - 3*PolyGamma(1, 1/3))/(12*sqrt(3)*Pi)) * sqrt(Gamma(1/3)/(2*Pi)) / A^4, where A = A074962 is the Glaisher-Kinkelin constant.

EXAMPLE

1.012378552722912249539602960496688692978044875869177150282...

MAPLE

evalf(product(exp(-1)*(1/(3*n)+1)^(3*n+1/2), n = 1..infinity), 104); # Vaclav Kotesovec, Aug 16 2015

MATHEMATICA

RealDigits[(3^(13/24)*E^(1 + (2*Pi^2 - 3*PolyGamma[1, 1/3])/(12*Sqrt[3]*Pi)) * Sqrt[Gamma[1/3]/(2*Pi)])/Glaisher^4, 10, 100][[1]] (* Vaclav Kotesovec, Aug 16 2015  after Eric W. Weisstein *)

N[Product[1/E*(1/(3*n) + 1)^(3*n + 1/2), {n, 1, Infinity}], 101] (* Vaclav Kotesovec, Aug 16 2015 *)

CROSSREFS

Cf. A074962.

Sequence in context: A199466 A199966 A011027 * A215722 A324777 A244162

Adjacent sequences:  A100069 A100070 A100071 * A100073 A100074 A100075

KEYWORD

nonn,cons

AUTHOR

Eric W. Weisstein, Nov 02 2004

STATUS

approved

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Last modified July 9 18:08 EDT 2020. Contains 335545 sequences. (Running on oeis4.)