A144655 Denominator of Sum_{k=1..n} k*H_{n+k} where H_m = Sum_{i=1..m}.

1, 2, 1, 1, 6, 4, 20, 5, 70, 56, 504, 420, 4620, 3960, 3432, 3003, 90090, 80080, 1361360, 408408, 369512, 67184, 470288, 1293292, 29745716, 27457584, 228813200, 212469400, 5736673800, 5354228880, 155272637520, 145568097675, 273491577450, 257403837600

Offset

0,2

Links

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

Example

0, 3/2, 6, 14, 155/6, 167/4, 1239/20, 433/5, 8109/70, 8389/56, ...

Maple

a:=n->add(k*add(1/i, i=1..n+k), k=1..n): seq(denom(a(n)), n=0..40); # Muniru A Asiru, Dec 03 2018

Mathematica

a[n_] := Denominator[Sum[k * 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*sum(i=1, n+k, 1/i))); \\ Michel Marcus, Dec 03 2018
(GAP) List(List([0..40], n->Sum([1..n], k->k*Sum([1..n+k], i->1/i))), DenominatorRat); # Muniru A Asiru, Dec 03 2018

Crossrefs

Suggested by A102720/A144653.

Cf. A001008, A002805, A144654.

Sequence in context: A047920 A350269 A249673 * A190782 A369288 A330490

Adjacent sequences: A144652 A144653 A144654 * A144656 A144657 A144658

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 28 2009

Status

approved