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A369766 Maximal coefficient of Product_{i=1..n} Sum_{j=0..i} x^(i*j).

%I A369766 #14 Jan 31 2024 13:11:06
%S A369766 1,1,1,2,6,24,115,662,4456,34323,298220,2885156,30760556,358379076,
%T A369766 4530375092,61762729722,903311893770,14108704577103,234387946711329,
%U A369766 4127027097703638,76774080851679152,1504640319524566870,30986929089570280955,669023741837953551188
%N A369766 Maximal coefficient of Product_{i=1..n} Sum_{j=0..i} x^(i*j).
%p A369766 a:= n-> max(coeffs(expand(mul(add(x^(i*j), j=0..i), i=1..n)))):
%p A369766 seq(a(n), n=0..23);  # _Alois P. Heinz_, Jan 31 2024
%t A369766 Table[Max[CoefficientList[Product[Sum[x^(i j), {j, 0, i}], {i, 1, n}], x]], {n, 0, 23}]
%o A369766 (PARI) a(n) = vecmax(Vec(prod(i=1, n, sum(j=0, i, x^(i*j))))); \\ _Michel Marcus_, Jan 31 2024
%o A369766 (Python)
%o A369766 from collections import Counter
%o A369766 def A369766(n):
%o A369766     c = {0:1,1:1}
%o A369766     for i in range(2,n+1):
%o A369766         d = Counter()
%o A369766         for k in c:
%o A369766             for j in range(0,i*i+1,i):
%o A369766                 d[j+k] += c[k]
%o A369766         c = d
%o A369766     return max(c.values()) # _Chai Wah Wu_, Jan 31 2024
%Y A369766 Cf. A000140, A025591, A052335.
%K A369766 nonn
%O A369766 0,4
%A A369766 _Ilya Gutkovskiy_, Jan 31 2024