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A027612
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Numerator of 1/n + 2/(n-1) + 3/(n-2) + ... + (n-1)/2 + n.
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29
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1, 5, 13, 77, 87, 223, 481, 4609, 4861, 55991, 58301, 785633, 811373, 835397, 1715839, 29889983, 30570663, 197698279, 201578155, 41054655, 13920029, 325333835, 990874363, 25128807667, 25472027467, 232222818803, 235091155703, 6897956948587, 6975593267347
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OFFSET
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1,2
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COMMENTS
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Numerator of a second-order harmonic number H(n, (2)) = Sum_{k=1..n} HarmonicNumber(k). - Alexander Adamchuk, Apr 12 2006
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LINKS
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FORMULA
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a(n) = numerators of coefficients in expansion of -log(1-x)/(1-x)^2.
a(n) = numerators of (n+1)*(harmonic(n+1) - 1).
a(n) = numerators of (n+1)*(Psi(n+2) + Euler-gamma - 1). (End)
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MAPLE
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a := n -> numer(add((n+1-j)/j, j=1..n));
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MATHEMATICA
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Numerator[Table[Sum[Sum[1/i, {i, 1, k}], {k, 1, n}], {n, 1, 30}]] (* Alexander Adamchuk, Apr 12 2006 *)
Numerator[Table[Sum[k/(n-k+1), {k, 1, n}], {n, 1, 50}]] (* Alexander Adamchuk, Jul 26 2006 *)
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PROG
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(Haskell)
import Data.Ratio ((%), numerator)
a027612 n = numerator $ sum $ zipWith (%) [1 .. n] [n, n-1 .. 1]
(PARI) a(n) = numerator(sum(k=1, n, k/(n-k+1))); \\ Michel Marcus, Jul 14 2018
(Magma) [Numerator((&+[j/(n-j+1): j in [1..n]])): n in [1..30]]; // G. C. Greubel, Aug 23 2022
(SageMath) [numerator(n*(harmonic_number(n+1) - 1)) for n in (1..30)] # G. C. Greubel, Aug 23 2022
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CROSSREFS
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KEYWORD
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nonn,easy,frac
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AUTHOR
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Glen Burch (gburch(AT)erols.com)
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STATUS
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approved
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