A374077 Expansion of Product_{k>=1} 1 / (1 + x^(5*k-2)).

1, 0, 0, -1, 0, 0, 1, 0, -1, -1, 0, 1, 1, -1, -1, -1, 2, 1, 0, -2, -1, 1, 2, 0, -2, -2, 2, 2, 1, -3, -2, 1, 4, 1, -3, -4, 2, 4, 3, -5, -5, 0, 7, 4, -4, -8, 0, 7, 8, -5, -9, -4, 10, 9, -3, -13, -5, 9, 14, -3, -14, -10, 12, 16, 1, -19, -12, 10, 23, 1, -20, -20, 13, 26, 8, -26

Offset: 0

Author

Ilya Gutkovskiy, Jun 27 2024

Keywords

• sign

Crossrefs

Cf. A081360, A081362, A109699, A281271, A284320, A374064, A374065, A374076, A374078, A374079.

Programs

Mathematica

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