A130895 Denominator 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, 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, 68908925685600, 11484820947600

Offset

1,3

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

Table of n, a(n) for n=1..28.

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.

Mathematica

f[n_] := Sum[ HarmonicNumber[k] HarmonicNumber[n + 1 - k], {k, n}]; Table[ Denominator@ f@n, {n, 26}] (* Robert G. Wilson v, Jul 02 2007 *)

Crossrefs

Cf. A130894.

Sequence in context: A112033 A248171 A258227 * A367431 A038329 A098909

Adjacent sequences: A130892 A130893 A130894 * A130896 A130897 A130898

Keyword

frac,nonn

Author

Leroy Quet, Jun 07 2007

Extensions

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

Status

approved