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A320900 Expansion of Sum_{k>=1} x^k/(1 + x^k)^3. 1
1, -2, 7, -12, 16, -17, 29, -48, 52, -42, 67, -105, 92, -79, 142, -184, 154, -143, 191, -262, 266, -189, 277, -441, 341, -262, 430, -495, 436, -402, 497, -712, 634, -444, 674, -897, 704, -553, 878, -1118, 862, -766, 947, -1189, 1222, -807, 1129, -1753, 1254, -992 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..50.

FORMULA

G.f.: Sum_{k>=1} (-1)^(k+1)*A000217(k)*x^k/(1 - x^k).

a(n) = Sum_{d|n} (-1)^(d+1)*d*(d + 1)/2.

a(n) = A000593(n) + A050999(n) - (A000203(n) + A001157(n))/2.

MAPLE

seq(coeff(series(add(x^k/(1+x^k)^3, k=1..n), x, n+1), x, n), n = 1 .. 50); # Muniru A Asiru, Oct 23 2018

MATHEMATICA

nmax = 50; Rest[CoefficientList[Series[Sum[x^k/(1 + x^k)^3, {k, 1, nmax}], {x, 0, nmax}], x]]

Table[Sum[(-1)^(d + 1) d (d + 1)/2, {d, Divisors[n]}], {n, 50}]

CROSSREFS

Cf. A000203, A000217, A000593, A001157, A002129, A007437, A050999, A064027, A320901.

Sequence in context: A266109 A006143 A190453 * A215247 A160455 A045929

Adjacent sequences:  A320897 A320898 A320899 * A320901 A320902 A320903

KEYWORD

sign

AUTHOR

Ilya Gutkovskiy, Oct 23 2018

STATUS

approved

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Last modified September 22 02:03 EDT 2021. Contains 347605 sequences. (Running on oeis4.)