A369791 a(n) is the maximal coefficient of (1 + x^a(1)) * (1 + x^a(1) + x^a(2)) * ... * (1 + x^a(1) + x^a(2) + ... + x^a(n-1)).

1, 1, 1, 3, 8, 22, 70, 262, 1088, 5076, 26490, 146542, 896402, 5662622, 39826304, 279072864, 2232912264, 17866212198, 153323343990, 1379920982310, 13115759159982, 131158174385100

Offset: 0

Author

Ilya Gutkovskiy, Feb 01 2024

Keywords

• nonn
• more

Crossrefs

Cf. A000140.

Programs

Mathematica

a[n_] := a[n] = Max[CoefficientList[Product[(1 + Sum[x^a[j], {j, 1, i}]), {i, 1, n - 1}], x]]; Table[a[n], {n, 0, 15}]

Python

from itertools import islice
from collections import Counter
def A369791_gen(): # generator of terms
    c, a = {0:1}, []
    while True:
        a.append(max(c.values()))
        yield a[-1]
        d = Counter(c)
        for k in c:
            for b in a:
                d[k+b] += c[k]
        c = d
A369791_list = list(islice(A369791_gen(),10)) # Chai Wah Wu, Feb 01 2024

Extensions

a(16)-a(20) from Alois P. Heinz, Feb 01 2024

a(21) from Chai Wah Wu, Feb 01 2024