A119787 Numerator of the product of n and the n-th alternating harmonic number, Sum_{k=1..n} (-1)^(k+1)/k.

1, 1, 5, 7, 47, 37, 319, 533, 1879, 1627, 20417, 18107, 263111, 237371, 261395, 95549, 1768477, 1632341, 33464927, 155685007, 166770367, 156188887, 3825136961, 3602044091, 19081066231, 18051406831, 57128792093, 54260455193

Offset

1,3

Comments

a(n) almost always equals A058313(n), which is the numerator of the n-th alternating harmonic number, Sum ((-1)^(k+1)/k, k=1..n), except for n = 15, 28, 75, 77, 104, ... The ratio a(n)/A058313(n) for n = 1..400 is given in A119788.

Links

Table of n, a(n) for n=1..28.

Formula

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

Example

The first few fractions are 1, 1, 5/2, 7/3, 47/12, 37/10, 319/60, 533/105, 1879/280, ... = A119787/A334721. - Petros Hadjicostas, May 08 2020

Mathematica

Numerator[Table[Sum[(-1)^(i+1)*n/i, {i, 1, n}], {n, 1, 50}]]

Prog

(PARI) a(n) = numerator(n*sum(k=1, n, (-1)^(k+1)/k)); \\ Michel Marcus, May 09 2020

Crossrefs

Cf. A058313, A119788, A334721 (denominators).

Sequence in context: A075830 A058313 A120301 * A025530 A106114 A217039

Adjacent sequences: A119784 A119785 A119786 * A119788 A119789 A119790

Keyword

frac,nonn

Author

Alexander Adamchuk, Jun 26 2006

Status

approved