A380499 Absolute value of the minimum coefficient of (1 - x)^2 * (1 - x^2)^2 * (1 - x^3)^2 * ... * (1 - x^n)^2.

1, 2, 2, 6, 4, 12, 8, 24, 19, 44, 36, 78, 74, 148, 156, 286, 322, 556, 682, 1120, 1448, 2308, 3072, 4784, 6538, 10064, 14001, 21296, 29928, 45276, 64032, 96712, 137520, 207156, 296236, 444748, 637812, 956884, 1373622, 2062080, 2968872, 4450120, 6422472, 9616202, 13894990, 20802836

Offset: 0

Author

Ilya Gutkovskiy, Jan 25 2025

Keywords

• nonn

Crossrefs

Cf. A002107, A047653, A086394, A133871, A369710.

Programs

Maple

p:= proc(n) option remember;
     `if`(n=0, 1, expand(p(n-1)*(1-x^n)^2))
    end:
a:= n-> abs(min(coeffs(p(n)))):
seq(a(n), n=0..45);  # Alois P. Heinz, Jan 25 2025

Mathematica

Table[Min[CoefficientList[Product[(1 - x^k)^2, {k, 1, n}], x]], {n, 0, 45}] // Abs

PARI

a(n) = abs(vecmin(Vec(prod(k=1, n, (1-x^k)^2)))); \\ Michel Marcus, Jan 25 2025