A388558 Decimal expansion of (2 * sqrt(2) * (-3+sqrt(3)) * Pi * Gamma(3/4)^3) / (Gamma(-1/3) * Gamma(7/12)^3 * Gamma(11/12)^2).

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

Offset

1,2

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} A113660(k) / exp(k*Pi).

Equals 3^(3/8) * sqrt(sqrt(3) - 1) * Gamma(1/4)^2 / (2^(5/4) * Pi^(3/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.2821561770895734610262231230391489489...

Mathematica

First[RealDigits[(2*Sqrt[2]*(-3 + Sqrt[3])*Pi*Gamma[3/4]^3)/(Gamma[-1/3]*Gamma[7/12]^3*Gamma[11/12]^2), 10, 100]]
RealDigits[3^(3/8)*Sqrt[Sqrt[3] - 1]*Gamma[1/4]^2 / (2^(5/4)*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (2/3) * Pi * 3^(1/2) * sqrt(2) * (3^(1/2)-1) * gamma(3/4)^3 / gamma(11/12)^2 / gamma(7/12)^3 / gamma(2/3)

Crossrefs

Cf. A113660.

Sequence in context: A329816 A194567 A351794 * A065813 A076344 A307450

Adjacent sequences: A388555 A388556 A388557 * A388559 A388560 A388561

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved