A294827 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.

2, 7, 252, 2142, 58905, 1060290, 16964640, 627691680, 627691680, 29501508960, 383519616480, 7286872713120, 225893054106720, 15134834625150240, 15134834625150240, 15134834625150240, 620528219631159840, 17995318369303635360, 413892322493983613280, 8029511056383282097632

Offset: 0

Author

Wolfdieter Lang, Nov 16 2017

Keywords

• nonn
• frac
• easy

Comments

The corresponding numerators are given in A294826. Details are found there.

Examples

			See A294826 for the rationals.
		

Crossrefs

Cf. A000566, A135706, A294826.

Programs

PARI

a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 2)))); \\ Michel Marcus, Nov 17 2017

Formula

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.