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A369764 Maximal coefficient of (1 - x) * (1 - x^8) * (1 - x^27) * ... * (1 - x^(n^3)).

%I A369764 #24 Jul 12 2025 08:34:32
%S A369764 1,1,1,1,1,1,2,2,2,3,3,4,7,7,7,8,11,18,23,28,32,40,55,58,81,118,128,
%T A369764 171,204,327,395,555,843,1009,1580,2254,3224,4703,6999,4573,6255,7760,
%U A369764 12563,15626,22328,33788,47750,51522,84103,120853,168565,312262,306080
%N A369764 Maximal coefficient of (1 - x) * (1 - x^8) * (1 - x^27) * ... * (1 - x^(n^3)).
%F A369764 Trivial bounds: 1 <= a(n) <= 2^n. - _Charles R Greathouse IV_, Jul 07 2025
%p A369764 b:= proc(n) b(n):= `if`(n=0, 1, expand(b(n-1)*(1-x^(n^3)))) end:
%p A369764 a:= n-> max(coeffs(b(n))):
%p A369764 seq(a(n), n=0..52);  # _Alois P. Heinz_, Jan 31 2024
%t A369764 b[n_] := b[n] = If[n == 0, 1, Expand[b[n-1]*(1-x^(n^3))]];
%t A369764 a[n_] := Max[CoefficientList[b[n], x]];
%t A369764 Table[a[n], {n, 0, 52}] (* _Jean-François Alcover_, Jul 07 2025, after _Alois P. Heinz_ *)
%o A369764 (PARI) a(n)=vecmax(Vec(prod(k=1,n,1-x^(k^3))));
%o A369764 vector(30,n,a(n-1)) \\ _Joerg Arndt_, Jan 31 2024
%o A369764 (Python)
%o A369764 from collections import Counter
%o A369764 def A369764(n):
%o A369764     c = {0:1,1:-1}
%o A369764     for i in range(2,n+1):
%o A369764         d = Counter(c)
%o A369764         for k in c:
%o A369764             d[k+i**3] -= c[k]
%o A369764         c = d
%o A369764     return max(c.values()) # _Chai Wah Wu_, Jan 31 2024
%Y A369764 Cf. A000578, A086376, A279484, A359319, A369728.
%K A369764 nonn
%O A369764 0,7
%A A369764 _Ilya Gutkovskiy_, Jan 31 2024
%E A369764 a(45)-a(52) from _Alois P. Heinz_, Jan 31 2024