A144653 Denominator of Sum_{k=1..n} k^2*H_{n+k} where H_m = Sum_{i=1..m}.

1, 2, 6, 15, 21, 126, 990, 1287, 15015, 102102, 75582, 1322685, 5148297, 12257850, 286833690, 29113619535, 24131609775, 5056146810, 158337229050, 135195634035, 4770474515235, 177808595567850, 155131557292530, 12798353476633725, 79057257761377467, 35057064527669646

Offset

0,2

Links

Muniru A Asiru, Table of n, a(n) for n = 0..1000

M. Kauers and C. Schneider, Indefinite summation with unspecified summands, Discr. Math., 306 (2006), 2073-2083. See Eq. 4.

Example

0, 3/2, 61/6, 499/15, 1657/21, 19627/126, 270271/990, 566414/1287, ...

Maple

a:=n->add(k^2*add(1/i, i=1..n+k), k=1..n): seq(denom(a(n)), n=0..30); # Muniru A Asiru, Dec 03 2018

Mathematica

a[n_] := Denominator[Sum[k^2 * HarmonicNumber[n+k], {k, 1, n}]]; Array[a, 30, 0] (* Amiram Eldar, Dec 03 2018 *)

Prog

(PARI) a(n) = denominator(sum(k=1, n, k^2*sum(i=1, n+k, 1/i))); \\ Michel Marcus, Dec 03 2018
(GAP) List(List([0..30], n->Sum([1..n], k->k^2*Sum([1..n+k], i->1/i))), DenominatorRat); # Muniru A Asiru, Dec 03 2018

Crossrefs

Cf. A001008, A002805, A102720.

Sequence in context: A129631 A014847 A013636 * A276782 A227210 A177442

Adjacent sequences: A144650 A144651 A144652 * A144654 A144655 A144656

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 28 2009

Status

approved