A363774 Expansion of 1/(Sum_{k>=0} x^(k^2))^2.

1, -2, 3, -4, 3, 0, -5, 12, -18, 18, -9, -12, 44, -76, 93, -76, 5, 120, -273, 400, -414, 228, 200, -828, 1480, -1842, 1539, -268, -2004, 4824, -7168, 7568, -4518, -2784, 13577, -24900, 31563, -27236, 6816, 30308, -77010, 116844, -126018, 80180, 34140, -205932, 389275

Offset: 0

Author

Seiichi Manyama, Jun 21 2023

Keywords

• sign
• easy

Crossrefs

Convolution inverse of A000925.

Column k=2 of A363778.

Cf. A162552, A274621.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec(1/sum(k=0, sqrtint(N), x^k^2)^2)

Formula

a(0) = 1; a(n) = -(2/n) * Sum_{k=1..n} A162552(k) * a(n-k).