A388604 Decimal expansion of ((-1+sqrt(3)) * Gamma(-1/12) * Gamma(3/4)) / (sqrt(6) * Gamma(-1/3)).

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

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} A132974(k) / exp(k*Pi).

Equals 2^(11/4) * Pi^(3/2) / (3^(3/8) * Gamma(1/4)^2 * sqrt(1 + sqrt(3))). - Vaclav Kotesovec, Jan 08 2026

Example

1.1419058312078545869592445134413563056...

Mathematica

First[RealDigits[((-1 + Sqrt[3])*Gamma[-1/12]*Gamma[3/4])/(Sqrt[6]*Gamma[-1/3]), 10, 100]]
RealDigits[2^(11/4)*Pi^(3/2) / (3^(3/8)*Gamma[1/4]^2*Sqrt[1 + Sqrt[3]]), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A132974.

Sequence in context: A177841 A141680 A141681 * A176215 A364016 A143469

Adjacent sequences: A388601 A388602 A388603 * A388605 A388606 A388607

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved