A388626 Decimal expansion of (1/32) * Gamma(2/3)^3 * Gamma(7/12)^3 * sqrt(2) * (1+3^(1/2))^3 / Gamma(3/4)^9.

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

Offset

1,2

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} A135763(k) / exp(k*Pi).

Equals (1 + sqrt(3))^(3/2) * Gamma(1/4)^6 / (2^(15/4) * 3^(9/8) * Pi^(9/2)). - Vaclav Kotesovec, Jan 08 2026

Example

1.2829841325889715647567117532838212556...

Mathematica

First[RealDigits[(Sqrt[26 + 15*Sqrt[3]]*Gamma[7/12]^3*Gamma[2/3]^3)/(8*Gamma[3/4]^9), 10, 100]]
RealDigits[(1 + Sqrt[3])^(3/2)*Gamma[1/4]^6/(2^(15/4)*3^(9/8)*Pi^(9/2)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (1/32) * gamma(2/3)^3 * gamma(7/12)^3 * sqrt(2) * (1+3^(1/2))^3 / gamma(3/4)^9

Crossrefs

Cf. A135763.

Sequence in context: A086396 A392156 A195844 * A222828 A222842 A098471

Adjacent sequences: A388623 A388624 A388625 * A388627 A388628 A388629

Keyword

nonn,cons

Author

Simon Plouffe, Sep 18 2025

Status

approved