A369766 Maximal coefficient of Product_{i=1..n} Sum_{j=0..i} x^(i*j).

1, 1, 1, 2, 6, 24, 115, 662, 4456, 34323, 298220, 2885156, 30760556, 358379076, 4530375092, 61762729722, 903311893770, 14108704577103, 234387946711329, 4127027097703638, 76774080851679152, 1504640319524566870, 30986929089570280955, 669023741837953551188

Offset: 0

Author

Ilya Gutkovskiy, Jan 31 2024

Keywords

• nonn

Crossrefs

Cf. A000140, A025591, A052335.

Programs

Maple

a:= n-> max(coeffs(expand(mul(add(x^(i*j), j=0..i), i=1..n)))):
seq(a(n), n=0..23);  # Alois P. Heinz, Jan 31 2024

Mathematica

Table[Max[CoefficientList[Product[Sum[x^(i j), {j, 0, i}], {i, 1, n}], x]], {n, 0, 23}]

PARI

a(n) = vecmax(Vec(prod(i=1, n, sum(j=0, i, x^(i*j))))); \\ Michel Marcus, Jan 31 2024

Python

from collections import Counter
def A369766(n):
    c = {0:1,1:1}
    for i in range(2,n+1):
        d = Counter()
        for k in c:
            for j in range(0,i*i+1,i):
                d[j+k] += c[k]
        c = d
    return max(c.values()) # Chai Wah Wu, Jan 31 2024