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A369983 Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

%I A369983 #11 Feb 07 2024 11:51:44
%S A369983 1,3,8,15,44,50,117,186,356,561,972,1761,3508,5789,10470,19023,35580,
%T A369983 62388,113418,205653,376496,674085,1226181,2211462,4056220,7287672,
%U A369983 13261764,24005627,43800562,79033269,143513301,260061408,473603594,855436899,1553736558,2813222766
%N A369983 Maximum of the absolute value of the coefficients of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.
%t A369983 Table[Max[Abs[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]]], {n, 0, 35}]
%o A369983 (PARI) a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^i)^3)))); \\ _Michel Marcus_, Feb 07 2024
%o A369983 (Python)
%o A369983 from collections import Counter
%o A369983 def A369983(n):
%o A369983     c = {0:1}
%o A369983     for k in range(1,n+1):
%o A369983         d = Counter(c)
%o A369983         for j in c:
%o A369983             a = c[j]
%o A369983             d[j+k] -= 3*a
%o A369983             d[j+2*k] += 3*a
%o A369983             d[j+3*k] -= a
%o A369983         c = d
%o A369983     return max(map(abs,c.values())) # _Chai Wah Wu_, Feb 07 2024
%Y A369983 Cf. A010816, A133871, A160089, A369709, A369711, A369790.
%K A369983 nonn
%O A369983 0,2
%A A369983 _Ilya Gutkovskiy_, Feb 07 2024