A388519 Decimal expansion of (3/2) * Gamma(2/3)^2 * Gamma(7/12)^2 * (2+3^(1/2)) * exp(-Pi / 2) / Pi / Gamma(3/4)^2.

1, 0, 5, 7, 0, 5, 0, 9, 1, 4, 2, 8, 0, 4, 4, 4, 8, 8, 7, 2, 6, 4, 5, 0, 2, 3, 3, 8, 0, 3, 0, 0, 4, 3, 4, 0, 1, 7, 1, 5, 3, 4, 7, 5, 6, 2, 5, 0, 0, 5, 2, 9, 1, 2, 5, 8, 3, 3, 2, 8, 0, 5, 5, 7, 7, 2, 0, 9, 2, 1, 8, 0, 8, 6, 9, 8, 2, 5, 7, 4, 3, 9, 9, 1, 1, 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} A112162(k) / exp(k*Pi).

Equals 2*sqrt(3 + 2*sqrt(3)) / exp(Pi/2). - Vaclav Kotesovec, Jan 08 2026

Example

1.0570509142804448872645023380300434017...

Mathematica

First[RealDigits[(24*(2 + Sqrt[3])*Exp[-1/2*Pi]*Gamma[7/12]^2*Gamma[2/3]^2)/(Pi*Gamma[-1/4]^2), 10, 100]]
RealDigits[2*Sqrt[3 + 2*Sqrt[3]] / E^(Pi/2), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

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

Crossrefs

Cf. A112162.

Sequence in context: A293506 A388563 A011350 * A295823 A161018 A393366

Adjacent sequences: A388516 A388517 A388518 * A388520 A388521 A388522

Keyword

nonn,cons

Author

Simon Plouffe, Sep 17 2025

Status

approved