A334580 Denominator of Sum_{k=1..n} (-1)^(k+1)/k^2.

1, 4, 36, 144, 3600, 1200, 58800, 235200, 6350400, 6350400, 768398400, 768398400, 129859329600, 129859329600, 129859329600, 519437318400, 150117385017600, 50039128339200, 18064125330451200, 3612825066090240, 3612825066090240, 3612825066090240, 1911184459961736960

Offset: 1

Author

Petros Hadjicostas, May 06 2020

Keywords

• nonn
• frac

Comments

For n = 1 to n = 19, we have a(n) = A068589(n), but a(20) = 3612825066090240 <> A068589(20) = 18064125330451200.

Examples

			The first few fractions are 1, 3/4, 31/36, 115/144, 3019/3600, 973/1200, 48877/58800, 191833/235200, 5257891/6350400, 5194387/6350400, ... = A119682/A334580.
		

Crossrefs

Cf. A068589, A119682 (numerators).

Programs

Maple

b := proc(n) local k: add((-1)^(k + 1)/k^2, k = 1 .. n): end proc:
seq(denom(b(n)), n=1..30);

PARI

a(n) = denominator(sum(k=1, n, (-1)^(k+1)/k^2)); \\ Michel Marcus, May 07 2020