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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

%I #8 Nov 22 2017 03:26:28

%S 1,14,546,20748,2593500,26799500,991581500,85276009000,5372388567000,

%T 59096274237000,3604872728457000,241526472806619000,

%U 17631432514883187000,1392883168675771773000,23679013867488120141000,47358027734976240282000,4593728690292695307354000,157718018366715872219154000

%N Denominators of the partial sums of the reciprocals of the positive tetradecagonal numbers (k + 1)*(6*k + 1) = A051866(k+1), for k >= 0.

%C The corresponding numerators are given in A294834. Details are found there.

%F 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.

%e See A294834 for the rationals.

%o (PARI) a(n) = denominator(sum(k=0, n, 1/((k + 1)*(6*k + 1)))); \\ _Michel Marcus_, Nov 21 2017

%Y Cf. A051866, A294834.

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Nov 20 2017

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Last modified September 7 12:42 EDT 2024. Contains 375730 sequences. (Running on oeis4.)