A388399 Decimal expansion of (8*2^(15/16) * (2+sqrt(2))^(5/4) * exp(Pi / 2) * Gamma(5/4)^3 * sin(Pi / 8)^3) / Pi^(9/4).

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

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} A034950(k) / exp(k*Pi).

Equals 8*2^(15/16)*(2 + sqrt(2))^(5/4)*exp(Pi/2)*Gamma(5/4)^3*sin(Pi/8)^3/Pi^(9/4). - Paolo Xausa, Sep 17 2025

Example

1.0864310224167481794245971342311255890...

Mathematica

First[RealDigits[8*2^(15/16)*(2 + Sqrt[2])^(5/4)*Exp[Pi/2]*Gamma[5/4]^3*Sin[Pi/8]^3/Pi^(9/4), 10, 100]] (* Paolo Xausa, Sep 17 2025 *)

Prog

(PARI) (1/32) * exp(Pi / 2) * 2^(15/16) * gamma(5/8)^3 * (2+2^(1/2))^(3/2) / (2^(1/2) * (2+2^(1/2))^(1/2))^(1/2) / Pi^(3/4) / gamma(7/8)^3

Crossrefs

Cf. A034950.

Sequence in context: A388107 A333198 A093019 * A388664 A388745 A175573

Adjacent sequences: A388396 A388397 A388398 * A388400 A388401 A388402

Keyword

nonn,cons

Author

Simon Plouffe, Sep 15 2025

Status

approved