A102720 Numerator of Sum_{k=1..n} k^2*H_{n+k} where H_m = Sum_{i=1..m}.

0, 3, 61, 499, 1657, 19627, 270271, 566414, 10013422, 98370749, 101287949, 2390592307, 12232312607, 37470326437, 1107461467873, 139734625012252, 141993136103452, 36029639090623, 1351662817439371, 1369250429650771, 56824258828125611, 2471493519758983073

Offset

0,2

Links

Table of n, a(n) for n=0..21.

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, ...

Mathematica

a[n_] := Numerator[Sum[k^2 * 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^2*sum(i=1, n+k, 1/i))); \\ Michel Marcus, Dec 03 2018

Crossrefs

Cf. A001008, A002805, A144653.

Sequence in context: A141979 A185831 A301666 * A120308 A279381 A186205

Adjacent sequences: A102717 A102718 A102719 * A102721 A102722 A102723

Keyword

nonn,frac

Author

N. J. A. Sloane, Jan 28 2009

Status

approved