A363775 Expansion of 1/(Sum_{k>=0} x^(k^2))^3.

1, -3, 6, -10, 12, -9, -2, 24, -54, 80, -84, 42, 66, -234, 420, -536, 450, -39, -740, 1770, -2688, 2898, -1722, -1320, 6078, -11349, 14736, -12992, 3084, 15999, -41212, 64032, -70788, 46020, 20778, -126132, 244120, -323421, 295410, -96848, -293868, 815829, -1297972

Offset: 0

Author

Seiichi Manyama, Jun 21 2023

Keywords

• sign
• easy

Crossrefs

Convolution inverse of A002102.

Column k=3 of A363778.

Cf. A162552.

Programs

PARI

my(N=50, x='x+O('x^N)); Vec(1/sum(k=0, sqrtint(N), x^k^2)^3)

Formula

a(0) = 1; a(n) = -(3/n) * Sum_{k=1..n} A162552(k) * a(n-k).