A388766 - OEIS

A388766

Decimal expansion of (sqrt(-8+14 / sqrt(3)) * Pi^2 * exp(Pi)) / (Gamma(-1/3)^2 * Gamma(7/12)^2 * Gamma(3/4)^2).

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

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OFFSET

1,3

LINKS

Table of n, a(n) for n=1..87.

Simon Plouffe, Numbers in the base e^Pi, 2025.

FORMULA

Empirical: Equals Sum_{k>=0} A214361(k) / exp(k*Pi).

Equals (sqrt(3) - 1) * exp(Pi) * Gamma(1/4)^4 / (16 * 3^(3/2) * Pi^3). - Vaclav Kotesovec, Jan 08 2026

EXAMPLE

1.1355085149716102483820776453810319980...

MATHEMATICA

First[RealDigits[(Sqrt[-8 + 14/Sqrt[3]]*Pi^2*Exp[Pi])/(Gamma[-1/3]^2*Gamma[7/12]^2*Gamma[3/4]^2), 10, 100]]

RealDigits[(Sqrt[3] - 1) * E^Pi * Gamma[1/4]^4 / (16 * 3^(3/2) * Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

PROG

(PARI) (1/54) * exp(Pi) * Pi^2 * sqrt(2) * 3^(3/4) * (3^(1/2)-1)^2 / gamma(7/12)^2 / gamma(2/3)^2 / gamma(3/4)^2

CROSSREFS

Cf. A214361.

Sequence in context: A284867 A343955 A152416 * A200334 A138112 A106233

Adjacent sequences: A388763 A388764 A388765 * A388767 A388768 A388769

KEYWORD

nonn,cons

AUTHOR

Simon Plouffe, Sep 18 2025

STATUS

approved