A102559 Denominator of the probability that (2n+1)-dimensional Gaussian random triangle has an obtuse angle.

4, 8, 20, 560, 560, 440, 7280, 160160, 2722720, 51731680, 51731680, 45762640, 1487285800, 5949143200, 86262576400, 10696559473600, 368846878400, 562976814400, 395772700523200, 395772700523200, 16226680721451200

Offset

1,1

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Gaussian Triangle Picking

Formula

From G. C. Greubel, Feb 01 2025: (Start)

a(n) = denominator( p(n) ), where p(n) = Pi/sqrt(3) - (3^(n+1)/2*binomial(2*n, n)) * Sum_{k >=0} binomial(2*k, k)*(3/16)^k/(2*k + 2*n + 1).

a(n) = denominator( p(n) ), where p(n) = Pi/sqrt(3) - (3^(n+1)/(2*(2*n+1)* binomial(2*n,n)) * Hypergeometric2F1([1/2, 1/2 + n], [3/2+n], 3/4). (End)

Example

1 - (3*sqrt(3))/(4*Pi), 1 - (9*sqrt(3))/(8*Pi), 1 - (27*sqrt(3))/(20*Pi), ...

Mathematica

Table[Denominator[Simplify[Pi/Sqrt[3] -(3^(n+1)*Hypergeometric2F1[1/2, 1/2+ n, 3/2+n, 3/4])/(2*(2*n+1)*Binomial[2*n, n])]], {n, 30}] (* G. C. Greubel, Feb 01 2025 *)

Crossrefs

Cf. A102556, A102557, A102558 (numerator).

Sequence in context: A168451 A000585 A209451 * A308233 A371001 A037020

Adjacent sequences: A102556 A102557 A102558 * A102560 A102561 A102562

Keyword

nonn,frac

Author

Eric W. Weisstein, Jan 14 2005

Status

approved