A294829 Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 3) = A147874(k+2), for k >= 0.

3, 48, 624, 1872, 215280, 1506960, 16576560, 39369330, 564293730, 9028699680, 478521083040, 4625703802720, 41631334224480, 707732681816160, 51664485772579680, 25832242886289840, 2144076159562056720, 357346026593676120, 3692575608134653240, 2584802925694257268

Offset: 0

Author

Wolfdieter Lang, Nov 16 2017

Keywords

• nonn
• frac
• easy

Comments

The corresponding numerators are given in A294828. Details are found there.

Examples

			For the rationals see A294828.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..891

Crossrefs

Cf. A147874, A294828, A294830.

Programs

Maple

map(denom,ListTools:-PartialSums([seq(1/(k+1)/(5*k+3),k=0..50)])); # Robert Israel, Nov 17 2017

PARI

a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 3)))); \\ Michel Marcus, Nov 17 2017

Formula

a(n) = denominator(V(5,3;n)) with V(5,3;n) = Sum_{k=0..n} 1/((k + 1)*(5*k + 3)) = Sum_{k=0..n} 1/A147874(k+2) = (1/2)*Sum_{k=0..n} (1/(k + 3/5) - 1/(k+1)). For this sum in terms of the digamma function see A294828.