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.

1, 14, 546, 20748, 2593500, 26799500, 991581500, 85276009000, 5372388567000, 59096274237000, 3604872728457000, 241526472806619000, 17631432514883187000, 1392883168675771773000, 23679013867488120141000, 47358027734976240282000, 4593728690292695307354000, 157718018366715872219154000

Offset: 0

Author

Wolfdieter Lang, Nov 20 2017

Keywords

• nonn
• frac
• easy

Comments

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

Examples

			See A294834 for the rationals.
		

Crossrefs

Cf. A051866, A294834.

Programs

PARI

a(n) = denominator(sum(k=0, n, 1/((k + 1)*(6*k + 1)))); \\ Michel Marcus, Nov 21 2017

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.