A144654 Numerator of Sum_{k=1..n} k*H_{n+k} where H_m = Sum_{i=1..m}.

0, 3, 6, 14, 155, 167, 1239, 433, 8109, 8389, 95051, 97571, 1298453, 1326173, 1351913, 1375937, 47547623, 48268343, 930031437, 314094559, 317974435, 64333911, 498634963, 1511424393, 38157431275, 38514379867, 349718397003, 352692968603, 10311277859587

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(numer(a(n)), n=0..30); # Muniru A Asiru, Dec 03 2018

Mathematica

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

Prog

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

Crossrefs

Suggested by A102720/A144653.

Cf. A001008, A002805, A144655.

Sequence in context: A129090 A324222 A058141 * A132279 A334042 A066107

Adjacent sequences: A144651 A144652 A144653 * A144655 A144656 A144657

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 28 2009

Status

approved