%I #15 Jan 06 2023 03:21:45

%S 1,1,1,3,6,5,30,105,140,126,1260,1155,13860,12870,12012,9009,72072,

%T 68068,1225224,5819814,5542680,5290740,116396280,111546435,535422888,

%U 514829700,1487285800,1434168450,5736673800,5545451340,166363540200,644658718275,312561802800

%N Denominator of rational part of raw moment n of the line point picking problem.

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

%F a(n) = denominator of 1 + (2*n)*Sum_{k = 1..n} (-1)^(n+k+1)/k. - _Peter Bala_, Jan 05 2023

%F a(n) = denominator of 2*n*((-1)^n*log(2) - LerchPhi(-1, 1, n + 1)) + 1. - _Peter Luschny_, Jan 05 2023

%e -1 + 2*log(2), 3 - 4*log(2), -4 + 6*log(2), 17/3 - 8*log(2), -41/6 + 10*log(2), ...

%p a := n -> denom(1 + 2*n*add((-1)^(n+k+1)/k, k = 1..n)):

%p seq(a(n), n = 1..30); # _Peter Bala_, Jan 05 2023

%p # Alternative:

%p a := n -> 2*n*((-1)^n*log(2) - LerchPhi(-1, 1, n + 1)) + 1:

%p seq(denom(simplify(a(n))), n = 1..33); # _Peter Luschny_, Jan 05 2023

%Y Cf. A058312, A058313, A115388.

%K nonn,frac,easy

%O 1,4

%A _Eric W. Weisstein_, Jan 21 2006