A369983 Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

1, 3, 8, 15, 44, 50, 117, 186, 356, 561, 972, 1761, 3508, 5789, 10470, 19023, 35580, 62388, 113418, 205653, 376496, 674085, 1226181, 2211462, 4056220, 7287672, 13261764, 24005627, 43800562, 79033269, 143513301, 260061408, 473603594, 855436899, 1553736558, 2813222766

Offset: 0

Author

Ilya Gutkovskiy, Feb 07 2024

Keywords

• nonn

Crossrefs

Cf. A010816, A133871, A160089, A369709, A369711, A369790.

Programs

Mathematica

Table[Max[Abs[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]]], {n, 0, 35}]

PARI

a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^i)^3)))); \\ Michel Marcus, Feb 07 2024

Python

from collections import Counter
def A369983(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            d[j+k] -= 3*a
            d[j+2*k] += 3*a
            d[j+3*k] -= a
        c = d
    return max(map(abs,c.values())) # Chai Wah Wu, Feb 07 2024