A388552 Decimal expansion of (2*2^(3/8) * sqrt((2+sqrt(2)) / Pi) * exp(Pi / 8) * Gamma(5/4)^2) / Pi.

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

Simon Plouffe, Numbers in the base e^Pi, 2025.

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A113407(k) / exp(k*Pi).

Example

1.04719121024548843802572142628355882148554833201262401089827634168236152814....

Mathematica

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

Prog

(PARI) (1/16) * exp(Pi / 8) * 2^(7/8) * gamma(5/8)^2 * (2+2^(1/2))^(3/2) / sqrt(Pi) / gamma(7/8)^2

Crossrefs

Cf. A113407.

Sequence in context: A335006 A085508 A198347 * A388436 A371333 A019670

Adjacent sequences: A388549 A388550 A388551 * A388553 A388554 A388555

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved