A369709 Maximal coefficient of (1 + x)^3 * (1 + x^2)^3 * (1 + x^3)^3 * ... * (1 + x^n)^3.

1, 3, 12, 62, 332, 1974, 12345, 80006, 531524, 3602358, 24836850, 173607568, 1226700784, 8748861828, 62922343566, 455805857978, 3321800235936, 24338840717799, 179217603427200, 1325490660318216, 9841000101286172, 73319407735938570, 548051770664957631, 4108826483323392880

Offset: 0

Author

Ilya Gutkovskiy, Jan 29 2024

Keywords

• nonn

Crossrefs

Cf. A022568, A025591, A047653.

Programs

Mathematica

Table[Max[CoefficientList[Product[(1 + x^k)^3, {k, 1, n}], x]], {n, 0, 23}]

PARI

a(n) = vecmax(Vec(prod(k=1, n, (1+x^k)^3))); \\ Michel Marcus, Jan 30 2024

Python

from collections import Counter
def A369709(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(c.values()) # Chai Wah Wu, Feb 07 2024