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A173756
Partial sums of A058313.
0
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.
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
KEYWORD
easy,nonn
AUTHOR
Jonathan Vos Post, Feb 23 2010
EXTENSIONS
Data corrected and extended by Petros Hadjicostas, May 06 2020
STATUS
approved