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

%I #11 Feb 07 2024 11:51:44

%S 1,3,8,15,44,50,117,186,356,561,972,1761,3508,5789,10470,19023,35580,

%T 62388,113418,205653,376496,674085,1226181,2211462,4056220,7287672,

%U 13261764,24005627,43800562,79033269,143513301,260061408,473603594,855436899,1553736558,2813222766

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

%o (PARI) a(n) = vecmax(apply(abs, Vec(prod(i=1, n, (1-x^i)^3)))); \\ _Michel Marcus_, Feb 07 2024

%o (Python)

%o from collections import Counter

%o def A369983(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(map(abs,c.values())) # _Chai Wah Wu_, Feb 07 2024

%Y Cf. A010816, A133871, A160089, A369709, A369711, A369790.

%K nonn

%O 0,2

%A _Ilya Gutkovskiy_, Feb 07 2024