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

1,4

Links

Table of n, a(n) for n=1..33.

Eric Weisstein's World of Mathematics, Line Point Picking

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

Example

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

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

Crossrefs

Cf. A058312, A058313, A115388.

Sequence in context: A328403 A199126 A247569 * A303564 A121867 A307132

Adjacent sequences: A115386 A115387 A115388 * A115390 A115391 A115392

Keyword

nonn,frac,easy

Author

Eric W. Weisstein, Jan 21 2006

Status

approved