A374076 Expansion of Product_{k>=1} 1 / (1 + x^(5*k-1)).

1, 0, 0, 0, -1, 0, 0, 0, 1, -1, 0, 0, -1, 1, -1, 0, 1, -1, 2, -1, -1, 1, -2, 2, 0, -1, 2, -3, 2, 0, -2, 3, -3, 2, 1, -3, 4, -4, 2, 2, -4, 5, -5, 1, 3, -6, 7, -5, 1, 5, -8, 8, -6, -1, 8, -10, 11, -6, -3, 10, -14, 12, -5, -6, 15, -17, 14, -4, -10, 19, -21, 15, -1, -15, 25, -25

Offset

0,19

Links

Table of n, a(n) for n=0..75.

Mathematica

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

Crossrefs

Cf. A081360, A081362, A109700, A281243, A284317, A374064, A374065, A374077, A374078, A374079.

Sequence in context: A175933 A175940 A299236 * A353970 A037827 A086074

Adjacent sequences: A374073 A374074 A374075 * A374077 A374078 A374079

Keyword

sign

Author

Ilya Gutkovskiy, Jun 27 2024

Status

approved