A363776 Expansion of 1/(Sum_{k>=0} x^(k^3))^2.

1, -2, 3, -4, 5, -6, 7, -8, 7, -4, -1, 8, -17, 28, -41, 56, -70, 80, -83, 76, -56, 20, 35, -112, 210, -324, 445, -562, 658, -712, 699, -590, 357, 22, -558, 1252, -2084, 3008, -3947, 4788, -5383, 5556, -5116, 3864, -1618, -1756, 6307, -11956, 18454, -25348, 31962, -37380

Offset: 0

Author

Seiichi Manyama, Jun 21 2023

Keywords

• sign
• easy

Crossrefs

Convolution inverse of A173677.

Column k=2 of A363779.

Cf. A363783.

Programs

PARI

my(N=60, x='x+O('x^N)); Vec(1/sum(k=0, N^(1/3), x^k^3)^2)

Formula

a(0) = 1; a(n) = -(2/n) * Sum_{k=1..n} A363783(k) * a(n-k).