A334735 Denominator of Sum_{k=1..n} k^2 / Product_{k=1..n} k^2.

1, 4, 18, 96, 2880, 518400, 181440, 135475200, 8778792960, 376233984000, 72425041920000, 4588850656051200, 47345284546560000, 217144413044342784000, 42750306318104985600000, 4974581098834034688000000, 70875936417673484697600000, 13663463022599094380003328000000

Offset: 1

Author

Petros Hadjicostas, May 09 2020

Keywords

• nonn
• frac

Examples

			The first few fractions are 1, 5/4, 7/18, 5/96, 11/2880, 91/518400, 1/181440, 17/135475200, 19/8778792960, ... = A125294/A334735.
		

Crossrefs

Cf. A125294 (numerators), A166602.

Programs

Mathematica

Table[Denominator[n*(n + 1)*(2*n + 1)/(6*(n!)^2)], {n, 1, 18}] (* Amiram Eldar, May 09 2020 *)

PARI

a(n) = denominator(sum(k=1, n, k^2)/prod(k=1, n, k^2)); \\ Michel Marcus, May 09 2020

Formula

a(n) = denominator(n*(n + 1)*(2*n + 1)/6/(n!)^2).