A388749 Decimal expansion of (1/24) * exp(Pi / 2) * Pi * 3^(1/4) * Gamma(2/3) * Gamma(7/12) * (1+3^(1/2)) / Gamma(3/4)^7.

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

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} A209939(k) / exp(k*Pi).

Equals sqrt(1 + sqrt(3)) * exp(Pi/2) * Gamma(1/4)^6 / (2^(19/4) * 3^(9/8) * Pi^(9/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.1295115985505156097346351204477164666...

Mathematica

First[RealDigits[((1 + Sqrt[3])*Pi*Exp[Pi/2]*Gamma[7/12]*Gamma[2/3])/(8*3^(3/4)*Gamma[3/4]^7), 10, 100]]
RealDigits[Sqrt[1 + Sqrt[3]]*E^(Pi/2)*Gamma[1/4]^6 / (2^(19/4)*3^(9/8)*Pi^(9/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/24) * exp(Pi / 2) * Pi * 3^(1/4) * gamma(2/3) * gamma(7/12) * (1+3^(1/2)) / gamma(3/4)^7

Crossrefs

Cf. A209939.

Sequence in context: A328619 A365108 A076930 * A309926 A011068 A078149

Adjacent sequences: A388746 A388747 A388748 * A388750 A388751 A388752

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved