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A115389
Denominator of rational part of raw moment n of the line point picking problem.
1
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
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
KEYWORD
nonn,frac,easy
AUTHOR
Eric W. Weisstein, Jan 21 2006
STATUS
approved