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A130894 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). 2
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..23.

FORMULA

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.

MATHEMATICA

f[n_] := Sum[ HarmonicNumber[k] HarmonicNumber[n + 1 - k], {k, n}]; Table[ Numerator@ f@n, {n, 24}] - Robert G. Wilson v, Jul 02 2007

CROSSREFS

Cf. A130895.

Sequence in context: A135951 A093245 A108231 * A254665 A106894 A166449

Adjacent sequences:  A130891 A130892 A130893 * A130895 A130896 A130897

KEYWORD

frac,nonn

AUTHOR

Leroy Quet, Jun 07 2007

EXTENSIONS

More terms from Robert G. Wilson v, Jul 02 2007

STATUS

approved

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Last modified May 10 01:30 EDT 2021. Contains 343747 sequences. (Running on oeis4.)