A388688 Decimal expansion of (1/64) * exp(9*Pi/8) * 2^(1/8) * Gamma(5/8)^3 * (2+sqrt(2))^(1/2) / Pi^(3/4) / Gamma(7/8)^3.

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

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} A180312(k) / exp(k*Pi).

Example

1.0433019009575321863821322561855424710...

Mathematica

First[RealDigits[(4*2^(3/8)*Sqrt[2 + Sqrt[2]]*Exp[(9*Pi)/8]*Gamma[5/4]^3*Sin[Pi/8]^3)/Pi^(9/4), 10, 100]]

Prog

(PARI) (1/64) * exp(9/8 * Pi) * 2^(1/8) * gamma(5/8)^3 * (2+2^(1/2))^(1/2) / Pi^(3/4) / gamma(7/8)^3

Crossrefs

Cf. A180312.

Sequence in context: A239799 A305235 A120011 * A177924 A200617 A016699

Adjacent sequences: A388685 A388686 A388687 * A388689 A388690 A388691

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved