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A294829
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Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 3) = A147874(k+2), for k >= 0.
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4
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3, 48, 624, 1872, 215280, 1506960, 16576560, 39369330, 564293730, 9028699680, 478521083040, 4625703802720, 41631334224480, 707732681816160, 51664485772579680, 25832242886289840, 2144076159562056720, 357346026593676120, 3692575608134653240, 2584802925694257268
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OFFSET
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0,1
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COMMENTS
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The corresponding numerators are given in A294828. Details are found there.
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LINKS
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FORMULA
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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.
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EXAMPLE
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MAPLE
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map(denom, ListTools:-PartialSums([seq(1/(k+1)/(5*k+3), k=0..50)])); # Robert Israel, Nov 17 2017
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PROG
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(PARI) a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 3)))); \\ Michel Marcus, Nov 17 2017
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CROSSREFS
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KEYWORD
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nonn,frac,easy
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AUTHOR
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STATUS
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approved
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