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Maximum coefficient of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.
4

%I #13 Feb 07 2024 11:51:33

%S 1,3,8,15,44,50,117,186,356,561,969,1761,3508,5789,10347,19023,35580,

%T 62388,111255,205653,376496,674085,1201809,2211462,4056220,7287672,

%U 13027698,24005627,43800562,79033269,141583272,260061408,473603594,855436899,1532383878,2813222766

%N Maximum coefficient of (1 - x)^3 * (1 - x^2)^3 * (1 - x^3)^3 * ... * (1 - x^n)^3.

%t Table[Max[CoefficientList[Product[(1 - x^k)^3, {k, 1, n}], x]], {n, 0, 35}]

%o (PARI) a(n) = vecmax(Vec(prod(i=1, n, (1-x^i)^3))); \\ _Michel Marcus_, Jan 29 2024

%o (Python)

%o from collections import Counter

%o def A369711(n):

%o c = {0:1}

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

%o d = Counter(c)

%o for j in c:

%o a = c[j]

%o d[j+k] -= 3*a

%o d[j+2*k] += 3*a

%o d[j+3*k] -= a

%o c = d

%o return max(c.values()) # _Chai Wah Wu_, Feb 07 2024

%Y Cf. A010816, A086376, A369709.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Jan 29 2024