A374078 Expansion of Product_{k>=1} 1 / (1 + x^(5*k-3)).

1, 0, -1, 0, 1, 0, -1, -1, 1, 1, -1, -1, 0, 1, 1, -1, -1, 0, 1, 1, -1, -2, 0, 2, 2, -2, -3, 1, 4, 1, -4, -3, 3, 4, 0, -5, -3, 4, 5, -1, -6, -3, 6, 6, -2, -8, -3, 8, 8, -5, -11, -2, 12, 8, -8, -13, 1, 15, 8, -12, -15, 3, 19, 7, -16, -17, 6, 23, 8, -22, -20, 11, 30, 5, -30, -22

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2024

Keywords

• sign

Crossrefs

Cf. A081360, A081362, A109698, A281272, A284319, A374064, A374065, A374076, A374077, A374079.

Programs

Mathematica

nmax = 75; CoefficientList[Series[Product[1/(1 + x^(5 k - 3)), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 2 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]