%I #11 Apr 14 2022 05:33:59

%S 1,1,1,4,31,1,13,224,17,151,1825,404,2429,7279,1079,6472,23303,863,

%T 155347,932060,207127,621377,7456549,184112,1104673,29826157,1472897,

%U 79536428,477218599,53024287,636291455,3817748696,282796201,848388601

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

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LineLinePicking.html">Line Line Picking</a>.

%F a(n) = numerator((2^(n+3)+(-1)^n*2*(3*n+5))/((n+1)*(n+2)*3^(n+2))). - _Amiram Eldar_, Apr 14 2022

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

%t 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 *)

%Y Cf. A103308 (denominators).

%K nonn,frac

%O 2,4

%A _Eric W. Weisstein_, Jan 28 2005