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A294827
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Denominators of the partial sums of the reciprocals of twice the heptagonal numbers (k + 1)*(5*k + 2) = A135706(k+1) = 2*A000566(k+1), for k >= 0.
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3
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2, 7, 252, 2142, 58905, 1060290, 16964640, 627691680, 627691680, 29501508960, 383519616480, 7286872713120, 225893054106720, 15134834625150240, 15134834625150240, 15134834625150240, 620528219631159840, 17995318369303635360, 413892322493983613280, 8029511056383282097632
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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 A294826. Details are found there.
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LINKS
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FORMULA
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a(n) = denominator(V(5,2;n)) with V(5,2;n) = Sum_{k=0..n} 1/((k + 1)*(5*k + 2)) = Sum_{k=0..n} 1/A135706(k+1) = (1/3)*Sum_{k=0..n} (1/(k + 2/5) - 1/(k+1)). For this formula in terms of the digamma function see A294826.
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EXAMPLE
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PROG
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(PARI) a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 2)))); \\ 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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