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Search: id:A130894
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| A130894 |
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Numerator 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, 3, 71, 29, 638, 349, 14139, 79913, 325421, 10418, 11302933, 13078889, 60461593, 15543383, 707713291, 5116885451, 1729792071433, 1726815331, 28878310103, 4284784940629, 102022822469387, 88130993047, 135875890206619
(list; graph; listen)
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OFFSET
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1,2
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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[ Numerator@ f@n, {n, 24}] - Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 02 2007
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CROSSREFS
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Cf. A130895.
Adjacent sequences: A130891 A130892 A130893 this_sequence A130895 A130896 A130897
Sequence in context: A135951 A093245 A108231 this_sequence A106894 A094458 A111649
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KEYWORD
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frac,nonn
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AUTHOR
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Leroy Quet (qq-quet(AT)mindspring.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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