A388529 Decimal expansion of (1/64) * 3^(3/4) * Gamma(2/3)^3 * Gamma(7/12)^3 * (1+3^(1/2))^3 / Gamma(3/4)^9.

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

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} A113261(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(3/2) * Gamma(1/4)^6 / (2^(21/4) * 3^(3/8) * Pi^(9/2)). - Vaclav Kotesovec, Jan 07 2026

Example

1.0339921289151129307577834521492490672...

Mathematica

First[RealDigits[3^(3/4)*Gamma[2/3]^3*Gamma[7/12]^3*(1 + Sqrt[3])^3/(64*Gamma[3/4]^9), 10, 100]] (* Paolo Xausa, Sep 18 2025 *)
RealDigits[(1 + Sqrt[3])^(3/2) * Gamma[1/4]^6 / (2^(21/4)*3^(3/8)*Pi^(9/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 07 2026 *)

Prog

(PARI) (1/64) * 3^(3/4) * gamma(2/3)^3 * gamma(7/12)^3 * (1+3^(1/2))^3 / gamma(3/4)^9

Crossrefs

Cf. A113261.

Sequence in context: A362046 A155686 A290300 * A201456 A392688 A372267

Adjacent sequences: A388526 A388527 A388528 * A388530 A388531 A388532

Keyword

nonn,cons

Author

Simon Plouffe, Sep 17 2025

Status

approved