A115389 Denominator of rational part of raw moment n of the line point picking problem.
1, 1, 1, 3, 6, 5, 30, 105, 140, 126, 1260, 1155, 13860, 12870, 12012, 9009, 72072, 68068, 1225224, 5819814, 5542680, 5290740, 116396280, 111546435, 535422888, 514829700, 1487285800, 1434168450, 5736673800, 5545451340, 166363540200, 644658718275, 312561802800
Offset: 1
Examples
-1 + 2*log(2), 3 - 4*log(2), -4 + 6*log(2), 17/3 - 8*log(2), -41/6 + 10*log(2), ...
Links
- Eric Weisstein's World of Mathematics, Line Point Picking
Programs
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Maple
a := n -> denom(1 + 2*n*add((-1)^(n+k+1)/k, k = 1..n)): seq(a(n), n = 1..30); # Peter Bala, Jan 05 2023 # Alternative: a := n -> 2*n*((-1)^n*log(2) - LerchPhi(-1, 1, n + 1)) + 1: seq(denom(simplify(a(n))), n = 1..33); # Peter Luschny, Jan 05 2023
Formula
a(n) = denominator of 1 + (2*n)*Sum_{k = 1..n} (-1)^(n+k+1)/k. - Peter Bala, Jan 05 2023
a(n) = denominator of 2*n*((-1)^n*log(2) - LerchPhi(-1, 1, n + 1)) + 1. - Peter Luschny, Jan 05 2023