A388553 Decimal expansion of (1/16) * exp(Pi / 2) * sqrt(2) * Gamma(5/8)^2 * (2+sqrt(2)) * (2-sqrt(2))^(1/2) / sqrt(Pi) / Gamma(7/8)^2.

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

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} A113411(k) / exp(k*Pi).

Example

1.0864385999834424647454267240410623140...

Mathematica

First[RealDigits[(2*Sqrt[(2 - Sqrt[2])/Pi]*Exp[Pi/2]*Gamma[5/4]^2)/Pi, 10, 100]]

Prog

(PARI) (1/16) * exp(Pi / 2) * sqrt(2) * gamma(5/8)^2 * (2+2^(1/2)) * (2-2^(1/2))^(1/2) / sqrt(Pi) / gamma(7/8)^2

Crossrefs

Cf. A113411.

Sequence in context: A296494 A388393 A261027 * A388781 A388629 A296041

Adjacent sequences: A388550 A388551 A388552 * A388554 A388555 A388556

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved