A120296 Numerator of Sum_{k=1..n} (-1)^(k+1)/k^4.

1, 15, 1231, 19615, 12280111, 4090037, 9824498837, 157151464517, 38193952437631, 7637983935923, 111835788321880643, 111830093529238643, 3194097388508809394723, 3194009594644356242723, 15970381078317764649391

Offset

1,2

Comments

p divides a(p-1) for prime p > 2 - similar to Wolstenholme's theorem for A007406(n) (= numerator of Sum_{k=1..n} 1/k^2) and for A007410(n) (= numerator of Sum_{k=1..n} 1/k^4).

Lim_{n -> infinity} a(n)/A334585(n) = A267315 = (7/8)*A013662. - Petros Hadjicostas, May 07 2020

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = numerator(Sum_{k=1..n} (-1)^(k+1)/k^4).

Example

The first few fractions are 1, 15/16, 1231/1296, 19615/20736, 12280111/12960000, 4090037/4320000, 9824498837/10372320000, ... = A120296/A334585. - Petros Hadjicostas, May 06 2020

Mathematica

Numerator[Table[Sum[(-1)^(k+1)/k^4, {k, 1, n}], {n, 1, 20}]]

Prog

(PARI) a(n) = numerator(sum(k=1, n, (-1)^(k+1)/k^4)); \\ Michel Marcus, May 07 2020

Crossrefs

Cf. A007406, A007410, A013662, A119682, A267315, A334585 (denominators).

Sequence in context: A206394 A354385 A098723 * A209679 A135810 A273967

Adjacent sequences: A120293 A120294 A120295 * A120297 A120298 A120299

Keyword

nonn,frac

Author

Alexander Adamchuk, Jul 10 2006

Extensions

Name edited by Petros Hadjicostas, May 07 2020

Status

approved