A173756 Partial sums of A058313.

1, 2, 7, 14, 61, 98, 417, 950, 2829, 4456, 24873, 42980, 306091, 543462, 595741, 691290, 2459767, 4092108, 37557035, 193242042, 360012409, 516201296, 4341338257, 7943382348, 27024448579, 45075855410, 102204647503, 109956141102, 346222803073, 571398562364

Offset

1,2

Comments

Partial sum of the numerator of the n-th alternating harmonic number.

Links

Table of n, a(n) for n=1..30.

Formula

a(n) = Sum_{i=1..n} A058313(i) = Sum_{i=1..n} numerator(Sum_{k=1..i} (-1)^(k+1)/k). [Corrected by Petros Hadjicostas and Michel Marcus, May 06 2020]

Maple

a := proc(n) local i, k:
add(numer(add((-1)^(k + 1)/k, k = 1 .. i)), i = 1 .. n): end proc:
seq(a(n), n = 1 .. 40); # Petros Hadjicostas, May 06 2020

Prog

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

Crossrefs

Cf. A001008 (numerator of the n-th harmonic number), A025530, A058312 (denominators of the underlying sequence), A058313, A075830.

Sequence in context: A192507 A018622 A018668 * A018684 A354506 A018732

Adjacent sequences: A173753 A173754 A173755 * A173757 A173758 A173759

Keyword

easy,nonn

Author

Jonathan Vos Post, Feb 23 2010

Extensions

Data corrected and extended by Petros Hadjicostas, May 06 2020

Status

approved