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

Author

Eric W. Weisstein, Jan 21 2006

Keywords

• nonn
• frac
• easy

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

Crossrefs

Cf. A058312, A058313, A115388.

Programs

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