A103307 Reduced numerators of the central moments of the distribution of random line segments picked on a unit line segment.

1, 1, 1, 4, 31, 1, 13, 224, 17, 151, 1825, 404, 2429, 7279, 1079, 6472, 23303, 863, 155347, 932060, 207127, 621377, 7456549, 184112, 1104673, 29826157, 1472897, 79536428, 477218599, 53024287, 636291455, 3817748696, 282796201, 848388601

Offset

2,4

Links

Table of n, a(n) for n=2..35.

Eric Weisstein's World of Mathematics, Line Line Picking.

Formula

a(n) = numerator((2^(n+3)+(-1)^n*2*(3*n+5))/((n+1)*(n+2)*3^(n+2))). - Amiram Eldar, Apr 14 2022

Example

1/18, 1/135, 1/135, 4/1701, 31/20412, 1/1458, 13/32805, 224/1082565, ...

Mathematica

a[n_] := Numerator[(2^(n + 3) + (-1)^n*2*(3*n + 5))/((n + 1)*(n + 2)*3^(n + 2))]; Array[a, 35, 2] (* Amiram Eldar, Apr 14 2022 *)

Crossrefs

Cf. A103308 (denominators).

Sequence in context: A201974 A221250 A119926 * A196248 A196246 A345274

Adjacent sequences: A103304 A103305 A103306 * A103308 A103309 A103310

Keyword

nonn,frac

Author

Eric W. Weisstein, Jan 28 2005

Status

approved