A320900 Expansion of Sum_{k>=1} x^k/(1 + x^k)^3.

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

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..10000

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.

Cf. A363022, A363615, A363630.

Sequence in context: A266109 A006143 A190453 * A215247 A160455 A045929

Adjacent sequences: A320897 A320898 A320899 * A320901 A320902 A320903

Keyword

sign,look

Author

Ilya Gutkovskiy, Oct 23 2018

Status

approved