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 A294835 Denominators of the partial sums of the reciprocals of the positive tetradecagonal numbers (k + 1)*(6*k + 1) = A051866(k+1), for k >= 0. 2
 1, 14, 546, 20748, 2593500, 26799500, 991581500, 85276009000, 5372388567000, 59096274237000, 3604872728457000, 241526472806619000, 17631432514883187000, 1392883168675771773000, 23679013867488120141000, 47358027734976240282000, 4593728690292695307354000, 157718018366715872219154000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS The corresponding numerators are given in A294834. Details are found there. LINKS Table of n, a(n) for n=0..17. FORMULA a(n) = denominator(V(6,1;n)) with V(6,1;n) = Sum_{k=0..n} 1/((k + 1)*(6*k + 1)) = Sum_{k=0..n} 1/A051866(k+1) = (1/5)*Sum_{k=0..n} (1/(k + 1/6) - 1/(k + 1)). For the formula in terms of the digamma function see A294834. EXAMPLE See A294834 for the rationals. PROG (PARI) a(n) = denominator(sum(k=0, n, 1/((k + 1)*(6*k + 1)))); \\ Michel Marcus, Nov 21 2017 CROSSREFS Cf. A051866, A294834. Sequence in context: A210029 A292966 A109773 * A205582 A217582 A002010 Adjacent sequences: A294832 A294833 A294834 * A294836 A294837 A294838 KEYWORD nonn,frac,easy AUTHOR Wolfdieter Lang, Nov 20 2017 STATUS approved

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Last modified August 15 04:38 EDT 2024. Contains 375172 sequences. (Running on oeis4.)