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A369767 Maximal coefficient of Product_{i=1..n} Sum_{j=0..n} x^(i*j).

%I A369767 #13 Jan 31 2024 13:11:21
%S A369767 1,1,2,6,31,231,2347,29638,449693,7976253,162204059,3722558272,
%T A369767 95221978299,2687309507102,82967647793153,2782190523572392,
%U A369767 100715040802229833,3914979746952224303,162662679830709439637,7194483479557973730982,337519906320930133470189
%N A369767 Maximal coefficient of Product_{i=1..n} Sum_{j=0..n} x^(i*j).
%p A369767 a:= n-> max(coeffs(expand(mul(add(x^(i*j), j=0..n), i=1..n)))):
%p A369767 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jan 31 2024
%t A369767 Table[Max[CoefficientList[Product[Sum[x^(i j), {j, 0, n}], {i, 1, n}], x]], {n, 0, 20}]
%o A369767 (PARI) a(n) = vecmax(Vec(prod(i=1, n, sum(j=0, n, x^(i*j))))); \\ _Michel Marcus_, Jan 31 2024
%o A369767 (Python)
%o A369767 from collections import Counter
%o A369767 def A369767(n):
%o A369767     c = {j:1 for j in range(n+1)}
%o A369767     for i in range(2,n+1):
%o A369767         d = Counter()
%o A369767         for k in c:
%o A369767             for j in range(0,i*n+1,i):
%o A369767                 d[j+k] += c[k]
%o A369767         c = d
%o A369767     return max(c.values()) # _Chai Wah Wu_, Jan 31 2024
%Y A369767 Cf. A000041, A025591, A077047.
%K A369767 nonn
%O A369767 0,3
%A A369767 _Ilya Gutkovskiy_, Jan 31 2024