A388691 Decimal expansion of (1/32768) * exp(21*Pi/8) * 2^(5/8) * Gamma(5/8)^7 * (2+sqrt(2))^(3/2) / Pi^(7/4) / Gamma(7/8)^7.

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

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} A182803(k) / exp(k*Pi).

Example

1.0472094699441565513701333025773056728...

Mathematica

First[RealDigits[(16*2^(7/8)*(2 + Sqrt[2])^(3/2)*Exp[(21*Pi)/8]*Gamma[5/4]^7*Sin[Pi/8]^7)/Pi^(21/4), 10, 100]]

Prog

(PARI) (1/32768) * exp(21/8 * Pi) * 2^(5/8) * gamma(5/8)^7 * (2+2^(1/2))^(3/2) / Pi^(7/4) / gamma(7/8)^7
(PARI) (2-sqrt(2))^2 * exp(21*Pi/8) * gamma(1/4)^7 / Pi^(21/4) / 2^(117/8) \\ Charles R Greathouse IV, Jul 26 2026

Crossrefs

Cf. A182803.

Sequence in context: A388094 A388461 A388775 * A388909 A388933 A388692

Adjacent sequences: A388688 A388689 A388690 * A388692 A388693 A388694

Keyword

nonn,cons,changed

Author

Simon Plouffe, Sep 18 2025

Status

approved