A294832 Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 4) = 2*A005476(k+1), for k >= 0.

4, 36, 252, 1197, 47880, 1388520, 23604840, 153431460, 843873030, 2953555605, 17721333630, 2091117368340, 33457877893440, 769531191549120, 28472654087317440, 2249339672898077760, 2249339672898077760, 200191230887928920640, 9408987851732659270080, 1881797570346531854016

Offset: 0

Author

Wolfdieter Lang, Nov 18 2017

Keywords

• nonn
• frac
• easy

Comments

The corresponding numerators are given in A294831. Details are found there.

Examples

			For the rationals V(5,4;n) see A294831.
		

Crossrefs

Cf. 2*A005476, A294831.

Programs

PARI

a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 4)))); \\ Michel Marcus, Nov 19 2017

Formula

a(n) = denominator(V(5,4;n)) with V(5,4;n) = Sum_{k=0..n} 1/((k + 1)*(5*k + 4)) = Sum_{k=0..n} 1/(2*A005476(k+1)) = Sum_{k=0..n} (1/(k + 4/5) - 1/(k+1)).

For this sum in terms of the digamma function Psi see A294831.