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A369709 Maximal coefficient of (1 + x)^3 * (1 + x^2)^3 * (1 + x^3)^3 * ... * (1 + x^n)^3.

%I A369709 #13 Feb 07 2024 11:51:14
%S A369709 1,3,12,62,332,1974,12345,80006,531524,3602358,24836850,173607568,
%T A369709 1226700784,8748861828,62922343566,455805857978,3321800235936,
%U A369709 24338840717799,179217603427200,1325490660318216,9841000101286172,73319407735938570,548051770664957631,4108826483323392880
%N A369709 Maximal coefficient of (1 + x)^3 * (1 + x^2)^3 * (1 + x^3)^3 * ... * (1 + x^n)^3.
%t A369709 Table[Max[CoefficientList[Product[(1 + x^k)^3, {k, 1, n}], x]], {n, 0, 23}]
%o A369709 (PARI) a(n) = vecmax(Vec(prod(k=1, n, (1+x^k)^3))); \\ _Michel Marcus_, Jan 30 2024
%o A369709 (Python)
%o A369709 from collections import Counter
%o A369709 def A369709(n):
%o A369709     c = {0:1}
%o A369709     for k in range(1,n+1):
%o A369709         d = Counter(c)
%o A369709         for j in c:
%o A369709             a = c[j]
%o A369709             d[j+k] += 3*a
%o A369709             d[j+2*k] += 3*a
%o A369709             d[j+3*k] += a
%o A369709         c = d
%o A369709     return max(c.values()) # _Chai Wah Wu_, Feb 07 2024
%Y A369709 Cf. A022568, A025591, A047653.
%K A369709 nonn
%O A369709 0,2
%A A369709 _Ilya Gutkovskiy_, Jan 29 2024