A388400 Decimal expansion of (8 * (4+3 * sqrt(2))^(1/8) * exp(Pi / 2) * Gamma(5/4)^4) / Pi^3.

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

Offset

1,3

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

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

Formula

Empirical: Equals Sum_{k>=0} A034951(k) / exp(k*Pi).

Equals 8*(4 + 3*sqrt(2))^(1/8)*exp(Pi/2)*Gamma(5/4)^4/Pi^3. - Paolo Xausa, Sep 17 2025

Example

1.0904887178758020353082533421242735475...

Mathematica

First[RealDigits[8*(4 + 3*Sqrt[2])^(1/8)*Exp[Pi/2]*Gamma[5/4]^4/Pi^3, 10, 100]] (* Paolo Xausa, Sep 17 2025 *)

Prog

(PARI) (1/32) * exp(Pi / 2) * 2^(3/16) * gamma(5/8)^4 * (3+2 * sqrt(2)) / (2-2^(1/2))^(1/4) / Pi / gamma(7/8)^4

Crossrefs

Cf. A034951.

Sequence in context: A196398 A388581 A388601 * A388391 A389042 A192932

Adjacent sequences: A388397 A388398 A388399 * A388401 A388402 A388403

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved