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Maximal coefficient of (1 - x) * (1 - x^8) * (1 - x^27) * ... * (1 - x^(n^3)).
2

%I #17 Jan 31 2024 13:10:54

%S 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 171,204,327,395,555,843,1009,1580,2254,3224,4703,6999,4573,6255,7760,

%U 12563,15626,22328,33788,47750,51522,84103,120853,168565,312262,306080

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

%p b:= proc(n) b(n):= `if`(n=0, 1, expand(b(n-1)*(1-x^(n^3)))) end:

%p a:= n-> max(coeffs(b(n))):

%p seq(a(n), n=0..52); # _Alois P. Heinz_, Jan 31 2024

%o (PARI) a(n)=vecmax(Vec(prod(k=1,n,1-x^(k^3))));

%o vector(30,n,a(n-1)) \\ _Joerg Arndt_, Jan 31 2024

%o (Python)

%o from collections import Counter

%o def A369764(n):

%o c = {0:1,1:-1}

%o for i in range(2,n+1):

%o d = Counter(c)

%o for k in c:

%o d[k+i**3] -= c[k]

%o c = d

%o return max(c.values()) # _Chai Wah Wu_, Jan 31 2024

%Y Cf. A000578, A086376, A279484, A359319, A369728.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Jan 31 2024

%E a(45)-a(52) from _Alois P. Heinz_, Jan 31 2024