A388391 Decimal expansion of (4 * sqrt((2+sqrt(2)) / Pi) * Gamma(5/4)^2) / Pi.

1, 0, 9, 0, 4, 9, 2, 5, 2, 0, 8, 2, 3, 0, 8, 3, 1, 5, 7, 7, 8, 3, 0, 6, 9, 4, 8, 1, 0, 5, 9, 9, 8, 2, 5, 9, 9, 8, 8, 8, 5, 9, 5, 8, 7, 3, 8, 4, 4, 4, 0, 2, 5, 7, 4, 7, 8, 4, 1, 3, 6, 2, 6, 7, 9, 3, 2, 6, 5, 3, 5, 3, 4, 9, 3, 1, 0, 3, 4, 6, 2, 9, 5, 2, 2, 4, 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} A033715(k) / exp(k*Pi).

Example

1.0904925208230831577830694810599825999...

Mathematica

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

Prog

(PARI) (1/8) * gamma(5/8)^2 * (2+2^(1/2))^(3/2) * sqrt(2) / sqrt(Pi) / gamma(7/8)^2

Crossrefs

Cf. A033715.

Sequence in context: A388581 A388601 A388400 * A389042 A192932 A388435

Adjacent sequences: A388388 A388389 A388390 * A388392 A388393 A388394

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved