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A144655 Denominator of Sum_{k=1..n} k*H_{n+k} where H_m = Sum_{i=1..m}. 2

%I

%S 1,2,1,1,6,4,20,5,70,56,504,420,4620,3960,3432,3003,90090,80080,

%T 1361360,408408,369512,67184,470288,1293292,29745716,27457584,

%U 228813200,212469400,5736673800,5354228880,155272637520,145568097675,273491577450,257403837600

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

%H Muniru A Asiru, <a href="/A144655/b144655.txt">Table of n, a(n) for n = 0..1000</a>

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

%p 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

%t a[n_] := Denominator[Sum[k * 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*sum(i=1, n+k, 1/i))); \\ _Michel Marcus_, Dec 03 2018

%o (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

%Y Suggested by A102720/A144653.

%Y Cf. A001008, A002805, A144654.

%K nonn,frac

%O 0,2

%A _N. J. A. Sloane_, Jan 28 2009

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Last modified April 9 04:05 EDT 2020. Contains 333343 sequences. (Running on oeis4.)