A374065 Expansion of Product_{k>=1} 1 / (1 + x^(3*k-2)).

1, -1, 1, -1, 0, 0, 0, -1, 2, -2, 1, 0, -1, 0, 2, -3, 3, -1, -1, 1, 1, -4, 5, -3, 0, 2, 0, -4, 7, -6, 1, 3, -2, -3, 9, -10, 4, 3, -5, -1, 11, -15, 10, 1, -8, 3, 10, -20, 17, -3, -10, 9, 7, -24, 26, -10, -10, 15, 2, -27, 37, -21, -8, 22, -6, -28, 49, -36, -2, 30, -19, -24, 61, -56, 10, 35

Offset

0,9

Links

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

Formula

a(0) = 1; a(n) = -Sum_{k=1..n} A261612(k) * a(n-k).

a(n) = Sum_{k=0..n} A081362(k) * A132462(n-k).

a(n) = Sum_{k=0..n} A109389(k) * A262928(n-k).

Mathematica

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

Crossrefs

Cf. A035382, A081360, A081362, A109389, A132462, A261612, A262928, A284312, A374064.

Sequence in context: A287397 A364204 A111407 * A084440 A179287 A016372

Adjacent sequences: A374062 A374063 A374064 * A374066 A374067 A374068

Keyword

sign

Author

Ilya Gutkovskiy, Jun 27 2024

Status

approved