A294965 Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(6*k + 5) = A049452(k+1).

5, 110, 5610, 258060, 1496748, 17462060, 715944460, 67298779240, 32101517697480, 378797908830264, 24621864073967160, 1748152349251668360, 1748152349251668360, 145096644987888473880, 2582720280784414835064, 490716853349038818662160, 49562402188252920684878160

Offset: 0

Author

Wolfdieter Lang, Nov 27 2017

Keywords

• nonn
• frac
• easy

Comments

The corresponding numerators are given in A294964. There details are found.

Examples

			For the rationals V(6,5;n) see A294964.
		

Links

• Robert Israel, Table of n, a(n) for n = 0..640

Crossrefs

Cf. A049452, A294964.

Programs

Maple

map(denom,  ListTools:-PartialSums([seq(1/(k+1)/(6*k+5),k=0..20)])); # Robert Israel, Nov 29 2017

PARI

a(n) = denominator(sum(k=0, n, 1/((k + 1)*(6*k + 5)))); \\ Michel Marcus, Nov 27 2017

Formula

a(n) = denominator(V(6,5;n)) with V(6,5;n) = Sum_{k=0..n} 1/((k + 1)*(6*k + 5)) = Sum_{k=0..n} 1/A049452(k+1) = Sum_{k=0..n} (1/(k + 5/6) - 1/(k + 1)).