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A115389
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Denominator of rational part of raw moment n of the line point picking problem.
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1
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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
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OFFSET
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1,4
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LINKS
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FORMULA
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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
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EXAMPLE
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-1 + 2*log(2), 3 - 4*log(2), -4 + 6*log(2), 17/3 - 8*log(2), -41/6 + 10*log(2), ...
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MAPLE
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a := n -> denom(1 + 2*n*add((-1)^(n+k+1)/k, k = 1..n)):
# 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
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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