A369987 Maximum of the absolute value of the coefficients of (1 - x) * (1 - x^8) * (1 - x^27) * ... * (1 - x^(n^3)).

1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 7, 7, 7, 8, 11, 18, 23, 28, 32, 40, 55, 58, 83, 118, 128, 171, 210, 327, 439, 555, 843, 1009, 1580, 2254, 3224, 4703, 6999, 4573, 6860, 7760, 12563, 15626, 24451, 33788, 48806, 51522, 84103, 120853, 171206, 312262, 306080, 464713, 657411, 892342

Offset

0,7

Links

Table of n, a(n) for n=0..55.

Mathematica

Table[Max[Abs[CoefficientList[Product[(1 - x^(k^3)), {k, 1, n}], x]]], {n, 0, 43}]

Prog

(PARI) a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^(i^3)))))); \\ Michel Marcus, Feb 07 2024
(Python)
from collections import Counter
def A369987(n):
    c = {0:1}
    for k in range(1, n+1):
        m, b = k**3, Counter(c)
        for j in c:
            b[j+m] -= c[j]
        c = b
    return max(map(abs, c.values())) # Chai Wah Wu, Feb 07 2024

Crossrefs

Cf. A000578, A160089, A279484, A359319, A369764, A369986.

Sequence in context: A369786 A275247 A369764 * A293440 A237121 A329493

Adjacent sequences: A369984 A369985 A369986 * A369988 A369990 A369991

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 07 2024

Extensions

More terms from Michel Marcus, Feb 07 2024

Status

approved