A388942 Decimal expansion of (32 * (4+3 * sqrt(2)) * (-3+sqrt(3)) * exp(Pi / 3) * Gamma(11/12) * Gamma(5/4)^3 * sin(Pi / 8)^3) / (Pi^2 * Gamma(-1/3)).

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

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} A263571(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(2)) * exp(Pi/3) * Gamma(1/4)^2 / (4 * 3^(3/8) * sqrt(1 + sqrt(3)) * Pi^(3/2)). - Vaclav Kotesovec, Jan 09 2026

Example

1.0471103540644912599561039393460192220...

Mathematica

First[RealDigits[(32*(4 + 3*Sqrt[2])*(-3 + Sqrt[3])*Exp[Pi/3]*Gamma[11/12]*Gamma[5/4]^3*Sin[Pi/8]^3)/(Pi^2*Gamma[-1/3]), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[2]] * E^(Pi/3) * Gamma[1/4]^2 / (4*3^(3/8)*Sqrt[1 + Sqrt[3]]*Pi^(3/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (1/48) * exp(Pi / 3) * 2^(1/4) * 3^(1/2) * gamma(5/8)^3 * gamma(11/12) * (2+2^(1/2))^2 * (3^(1/2)-1) / sqrt(Pi) / gamma(2/3) / gamma(7/8)^3

Crossrefs

Cf. A263571.

Sequence in context: A303173 A285778 A147864 * A195789 A390245 A367608

Adjacent sequences: A388939 A388940 A388941 * A388943 A388944 A388945

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved