A388461 Decimal expansion of (-1/72) * exp(35*Pi/24) * Pi^(7/4) * 2^(17/24) * Gamma(11/12)^2 * (-2+3^(1/2)) / Gamma(3/4)^7 / Gamma(5/6).

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

Offset

1,3

Links

Table of n, a(n) for n=1..87.

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

Index entries for transcendental numbers.

Formula

Empirical: Equals Sum_{k>=0} A081622(k) / exp(k*Pi).

Equals (sqrt(3) - 1) * exp(35*Pi/24) * Gamma(1/4)^5 / (288 * 2^(5/8) * 3^(1/4) * Pi^(15/4)). - Vaclav Kotesovec, Jan 08 2026

Example

1.04720942912688455946955692204957485859801694390227077380695004650891164943....

Mathematica

First[RealDigits[-1/36*((-2 + Sqrt[3])*Pi^(9/4)*Exp[(35*Pi)/24]*Gamma[11/12])/(2^(1/8)*Gamma[5/12]*Gamma[3/4]^7), 10, 100]]
RealDigits[(Sqrt[3] - 1) * E^(35*Pi/24) * Gamma[1/4]^5 / (288 * 2^(5/8) * 3^(1/4) * Pi^(15/4)), 10, 100][[1]] (* Vaclav Kotesovec, Jan 08 2026 *)

Prog

(PARI) (-1/72) * exp(35/24 * Pi) * Pi^(7/4) * 2^(17/24) * gamma(11/12)^2 * (-2+3^(1/2)) / gamma(3/4)^7 / gamma(5/6)
(PARI) (sqrt(3)-1)/288/2^(5/8)/3^(1/4)*exp(35*Pi/24)*gamma(1/4)^5/Pi^(15/4) \\ Charles R Greathouse IV, Jul 11 2026

Crossrefs

Cf. A081622.

Sequence in context: A388512 A246710 A388094 * A388775 A388691 A388909

Adjacent sequences: A388458 A388459 A388460 * A388462 A388463 A388464

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 17 2025

Status

approved