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A294829 Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 3) = A147874(k+2), for k >= 0. 4

%I #10 Nov 17 2017 20:35:49

%S 3,48,624,1872,215280,1506960,16576560,39369330,564293730,9028699680,

%T 478521083040,4625703802720,41631334224480,707732681816160,

%U 51664485772579680,25832242886289840,2144076159562056720,357346026593676120,3692575608134653240,2584802925694257268

%N Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 3) = A147874(k+2), for k >= 0.

%C The corresponding numerators are given in A294828. Details are found there.

%H Robert Israel, <a href="/A294829/b294829.txt">Table of n, a(n) for n = 0..891</a>

%F a(n) = denominator(V(5,3;n)) with V(5,3;n) = Sum_{k=0..n} 1/((k + 1)*(5*k + 3)) = Sum_{k=0..n} 1/A147874(k+2) = (1/2)*Sum_{k=0..n} (1/(k + 3/5) - 1/(k+1)). For this sum in terms of the digamma function see A294828.

%e For the rationals see A294828.

%p map(denom,ListTools:-PartialSums([seq(1/(k+1)/(5*k+3),k=0..50)])); # _Robert Israel_, Nov 17 2017

%o (PARI) a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 3)))); \\ _Michel Marcus_, Nov 17 2017

%Y Cf. A147874, A294828, A294830.

%K nonn,frac,easy

%O 0,1

%A _Wolfdieter Lang_, Nov 16 2017

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Last modified March 28 20:05 EDT 2024. Contains 371254 sequences. (Running on oeis4.)