A369773 Maximal coefficient of (1 + x) * (1 + x - x^2) * ... * (1 + x - x^2 + ... - (-x)^n).

1, 1, 2, 3, 4, 6, 19, 59, 233, 1189, 7046, 45326, 356517, 3108808, 30028121, 325635647, 3830546752, 49403859787, 685063715374, 10162709827329, 162776892315940, 2754021620252692, 49463507801582609, 940216720983170113, 18786988751008626812

Offset: 0

Author

Ilya Gutkovskiy, Jan 31 2024

Keywords

• nonn

Crossrefs

Cf. A000140, A039828, A039909, A369705, A369774.

Programs

Mathematica

Table[Max[CoefficientList[Product[(1 - Sum[(-x)^j, {j, 1, i}]), {i, 1, n}], x]], {n, 0, 24}]

Python

from collections import Counter
def A369773(n):
    c = {0:1}
    for k in range(1,n+1):
        d = Counter(c)
        for j in c:
            a = c[j]
            for i in range(1,k+1):
                d[j+i] += (a if i&1 else -a)
        c = d
    return max(c.values()) # Chai Wah Wu, Feb 01 2024