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Search: id:A130895
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| A130895 |
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Denominator of sum{k=1 to n} H(k)*H(n+1-k), where H(k) is the k-th harmonic number (sum{j=1 to k} 1/j). |
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+0
2
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| 1, 1, 12, 3, 45, 18, 560, 2520, 8400, 225, 207900, 207900, 840840, 191100, 7761600, 50450400, 15437822400, 14034384, 214885440, 29331862560, 645300976320, 517068090, 742096122768, 463810076730, 4466319257400, 492206612040
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OFFSET
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1,3
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COMMENT
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A130894(n)/A130895(n) also equals 2*sum{k=1 to n} H(k)*(n+1-k)/(k+1) = sum{k=1 to n} H(2,k)/(n+1-k), where H(2,k) = sum{j=1 to k} H(j) = (k+1)H(k) -k.
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FORMULA
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A130894(n)/A130895(n) = (n+2)*(2 - 2*H(n+2) +(H(n+2))^2 - G(n+2)), where G(n) = sum{k=1 to n} 1/k^2.
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MATHEMATICA
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f[n_] := Sum[ HarmonicNumber[k] HarmonicNumber[n + 1 - k], {k, n}]; Table[ Denominator@ f@n, {n, 26}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 02 2007
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CROSSREFS
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Cf. A130894.
Sequence in context: A063609 A040139 A112033 this_sequence A038329 A098909 A010202
Adjacent sequences: A130892 A130893 A130894 this_sequence A130896 A130897 A130898
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jun 07 2007
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 02 2007
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