A369774 Maximal coefficient of (1 - x) * (1 - x - x^2) * ... * (1 - x - x^2 - ... - x^n).

1, 1, 1, 2, 3, 8, 13, 63, 167, 1227, 5240, 46958, 297080, 3108808, 26714243, 325635647, 3535022425, 49403859787, 646713449897, 10221697892707, 156049674957354, 2756431502525358, 48028121269507891, 940216720983170113, 18359095114316009613

Offset: 0

Author

Ilya Gutkovskiy, Jan 31 2024

Keywords

• nonn

Crossrefs

Cf. A000140, A039909, A086376, A369773.

Programs

Mathematica

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

PARI

a(n) = vecmax(Vec(prod(k=1, n, 1 - sum(i=1, k, x^i)))); \\ Michel Marcus, Feb 01 2024

Python

from collections import Counter
def A369774(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
        c = d
    return max(c.values()) # Chai Wah Wu, Feb 01 2024