A369767 Maximal coefficient of Product_{i=1..n} Sum_{j=0..n} x^(i*j).

1, 1, 2, 6, 31, 231, 2347, 29638, 449693, 7976253, 162204059, 3722558272, 95221978299, 2687309507102, 82967647793153, 2782190523572392, 100715040802229833, 3914979746952224303, 162662679830709439637, 7194483479557973730982, 337519906320930133470189

Offset: 0

Author

Ilya Gutkovskiy, Jan 31 2024

Keywords

• nonn

Crossrefs

Cf. A000041, A025591, A077047.

Programs

Maple

a:= n-> max(coeffs(expand(mul(add(x^(i*j), j=0..n), i=1..n)))):
seq(a(n), n=0..20);  # Alois P. Heinz, Jan 31 2024

Mathematica

Table[Max[CoefficientList[Product[Sum[x^(i j), {j, 0, n}], {i, 1, n}], x]], {n, 0, 20}]

PARI

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

Python

from collections import Counter
def A369767(n):
    c = {j:1 for j in range(n+1)}
    for i in range(2,n+1):
        d = Counter()
        for k in c:
            for j in range(0,i*n+1,i):
                d[j+k] += c[k]
        c = d
    return max(c.values()) # Chai Wah Wu, Jan 31 2024