A130894 Numerator of Sum_{k=1..n} H(k)*H(n+1-k), where H(k) is the k-th harmonic number (Sum_{j=1..k} 1/j).

1, 3, 71, 29, 638, 349, 14139, 79913, 325421, 10418, 11302933, 13078889, 60461593, 15543383, 707713291, 5116885451, 1729792071433, 1726815331, 28878310103, 4284784940629, 102022822469387, 88130993047, 135875890206619, 90931468191287, 934812181407337

Offset

1,2

Comments

A130894(n)/A130895(n) also equals 2*Sum_{k=1..n} H(k)*(n+1-k)/(k+1) = Sum_{k=1..n} H(2,k)/(n+1-k), where H(2,k) = Sum_{j=1..k} H(j) = (k+1)*H(k) - k.

Links

Robert Israel, Table of n, a(n) for n = 1..1520

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..n} 1/k^2.

Maple

R:= [seq(1/i, i=1..100)]:
S:= ListTools:-PartialSums(R):
f:= proc(n) local k; numer(add(S[k]*S[n+1-k], k=1..n)): end proc:
map(f, [$1..100]); # Robert Israel, Feb 27 2022

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. A001008, A002805, A130895.

Sequence in context: A361254 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