A388966 Decimal expansion of (3/16) * 3^(1/2) * Gamma(2/3)^2 * Gamma(11/12)^3 * Gamma(7/12)^5 * (2+3^(1/2)) * exp(-Pi/6) / Gamma(3/4)^12.

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

Offset

1,3

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} A280384(k) / exp(k*Pi).

Equals (1 + sqrt(3)) * Gamma(1/4)^4 / (8*exp(Pi/6)*Pi^3). - Vaclav Kotesovec, Jan 09 2026

Example

1.1273983833580575174743286983934694477...

Mathematica

First[RealDigits[(3*(3 + 2*Sqrt[3])*Exp[-1/6*Pi]*Gamma[7/12]^5*Gamma[2/3]^2*Gamma[11/12]^3)/(16*Gamma[3/4]^12), 10, 100]]
RealDigits[(1 + Sqrt[3])*Gamma[1/4]^4 / (8*E^(Pi/6)*Pi^3), 10, 100][[1]] (* Vaclav Kotesovec, Jan 09 2026 *)

Prog

(PARI) (3/16) * 3^(1/2) * gamma(2/3)^2 * gamma(11/12)^3 * gamma(7/12)^5 * (2+3^(1/2)) * exp(-1/6 * Pi) / gamma(3/4)^12

Crossrefs

Cf. A280384.

Sequence in context: A387022 A256614 A021369 * A340711 A242304 A227415

Adjacent sequences: A388963 A388964 A388965 * A388967 A388968 A388969

Keyword

nonn,cons

Author

Simon Plouffe, Sep 21 2025

Status

approved