A320900 - OEIS

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

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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