A374079 Expansion of Product_{k>=1} 1 / (1 + x^(5*k-4)).

1, -1, 1, -1, 1, -1, 0, 0, 0, 0, 0, -1, 2, -2, 2, -2, 1, 0, -1, 1, -1, 0, 2, -3, 4, -4, 3, -1, -1, 2, -3, 2, 1, -4, 6, -7, 7, -4, 0, 3, -5, 5, -2, -3, 8, -11, 12, -9, 3, 3, -8, 10, -7, 0, 8, -15, 19, -17, 9, 1, -10, 16, -15, 6, 7, -19, 28, -29, 20, -5, -11, 23, -26, 17, 1, -21

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2024

Keywords

• sign

Crossrefs

Cf. A081360, A081362, A109697, A280454, A284314, A374064, A374065, A374076, A374077, A374078.

Programs

Mathematica

nmax = 75; CoefficientList[Series[Product[1/(1 + x^(5 k - 4)), {k, 1, nmax}], {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = (1/n) Sum[DivisorSum[k, (-1)^(k/#) # &, Mod[#, 5] == 1 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 75}]