A102558 Numerator of the probability that (2n+1)-dimensional Gaussian random triangle has an obtuse angle.

3, 9, 27, 837, 891, 729, 12393, 277749, 4782969, 91703097, 92293587, 82019061, 2674388259, 10722885057, 155747819547, 19336668383673, 667382013477, 1019303306559, 716912704223253, 717162977859147, 29411190301301847

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) = numerator( 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) = numerator( 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[Numerator[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, 40}] (* G. C. Greubel, Feb 01 2025 *)

Crossrefs

Cf. A102556, A102557, A102559 (denominator).

Sequence in context: A061582 A175129 A336793 * A361986 A022767 A015638

Adjacent sequences: A102555 A102556 A102557 * A102559 A102560 A102561

Keyword

nonn,frac

Author

Eric W. Weisstein, Jan 14 2005

Status

approved