A294521 Denominators of the partial sums of the reciprocals of the dodecagonal numbers (k + 1)*(5*k + 1) = A051624(k+1), for k >= 0.

1, 12, 44, 704, 73920, 320320, 9929920, 89369280, 3664140480, 84275231040, 1432678927680, 1432678927680, 87393414588480, 87393414588480, 6204932435782080, 14736714534982440, 132630430814841960, 5703108525038204280, 5703108525038204280, 18249947280122253696, 1843244675292347623296

Offset: 0

Author

Wolfdieter Lang, Nov 15 2017

Keywords

• nonn
• frac
• easy

Comments

The corresponding numerators are given in A294520. Details are found there.

Examples

			See A294520 for the rationals.
		

Crossrefs

Cf. A294520.

Programs

PARI

a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 1)))); \\ Michel Marcus, Nov 15 2017

Formula

a(n) = denominator(V(5,1;n)) with V(5,1;n) = Sum_{k=0..n} 1/((k + 1)*(5*k + 1)) = Sum_{k=0..n} 1/A051624(k+1) = (1/4)*Sum_{k=0..n} (1/(k + 1/5) - 1/(k+1)). For the formula in terms of the digamma function see A294520.