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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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18
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Numerator of a second order harmonic number H(n, (2)) = Sum[HarmonicNumber[k], {k, 1, n}]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
p divides a(p-3) for prime p>3. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 06 2006
Denominator is A027611(n+1). p divides a(p-3) for prime p>3. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 26 2006
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics. Harmonic Number.
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FORMULA
| Numerators of coefficients in expansion of -ln(1-x)/(1-x)^2. Numerators of (n+1)*(harmonic(n+1)-1). Numerators of (n+1)*(Psi(n+2)+gamma-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 02 2002
a(n) = Sum[Sum[1/i,{i,1,k}],{k,1,n}] - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
a(n) = Numerator[Sum[k/(n-k+1),{k,1,n}]]. - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 26 2006
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MAPLE
| ZL:=n->sum(sum(1/i, i=2..n), j=1..n): a:=n->floor(numer(ZL(n))): seq(a(n), n=2..27); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 14 2007
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MATHEMATICA
| Numerator[Table[Sum[Sum[1/i, {i, 1, k}], {k, 1, n}], {n, 1, 30}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Apr 12 2006
Numerator[Table[Sum[k/(n-k+1), {k, 1, n}], {n, 1, 50}]] - Alexander Adamchuk (alex(AT)kolmogorov.com), Jul 26 2006
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CROSSREFS
| Cf. A027611.
Cf. A001008, A002805, A001705, A006675.
Cf. A093418.
Sequence in context: A163732 A064169 A081525 * A027457 A113876 A096280
Adjacent sequences: A027609 A027610 A027611 * A027613 A027614 A027615
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KEYWORD
| nonn,easy,frac
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AUTHOR
| Glen Burch (gburch(AT)erols.com)
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