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%I #12 Dec 03 2018 18:31:42
%S 1,2,6,15,21,126,990,1287,15015,102102,75582,1322685,5148297,12257850,
%T 286833690,29113619535,24131609775,5056146810,158337229050,
%U 135195634035,4770474515235,177808595567850,155131557292530,12798353476633725,79057257761377467,35057064527669646
%N Denominator of Sum_{k=1..n} k^2*H_{n+k} where H_m = Sum_{i=1..m}.
%H Muniru A Asiru, <a href="/A144653/b144653.txt">Table of n, a(n) for n = 0..1000</a>
%H M. Kauers and C. Schneider, <a href="https://doi.org/10.1016/j.disc.2006.04.005">Indefinite summation with unspecified summands</a>, Discr. Math., 306 (2006), 2073-2083. See Eq. 4.
%e 0, 3/2, 61/6, 499/15, 1657/21, 19627/126, 270271/990, 566414/1287, ...
%p 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
%t a[n_] := Denominator[Sum[k^2 * HarmonicNumber[n+k], {k,1,n}]]; Array[a, 30, 0] (* _Amiram Eldar_, Dec 03 2018 *)
%o (PARI) a(n) = denominator(sum(k=1, n, k^2*sum(i=1, n+k, 1/i))); \\ _Michel Marcus_, Dec 03 2018
%o (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
%Y Cf. A001008, A002805, A102720.
%K nonn,frac
%O 0,2
%A _N. J. A. Sloane_, Jan 28 2009
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