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

%I #13 Jan 31 2024 13:11:21

%S 1,1,2,6,31,231,2347,29638,449693,7976253,162204059,3722558272,

%T 95221978299,2687309507102,82967647793153,2782190523572392,

%U 100715040802229833,3914979746952224303,162662679830709439637,7194483479557973730982,337519906320930133470189

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

%p a:= n-> max(coeffs(expand(mul(add(x^(i*j), j=0..n), i=1..n)))):

%p seq(a(n), n=0..20); # _Alois P. Heinz_, Jan 31 2024

%t Table[Max[CoefficientList[Product[Sum[x^(i j), {j, 0, n}], {i, 1, n}], x]], {n, 0, 20}]

%o (PARI) a(n) = vecmax(Vec(prod(i=1, n, sum(j=0, n, x^(i*j))))); \\ _Michel Marcus_, Jan 31 2024

%o (Python)

%o from collections import Counter

%o def A369767(n):

%o c = {j:1 for j in range(n+1)}

%o for i in range(2,n+1):

%o d = Counter()

%o for k in c:

%o for j in range(0,i*n+1,i):

%o d[j+k] += c[k]

%o c = d

%o return max(c.values()) # _Chai Wah Wu_, Jan 31 2024

%Y Cf. A000041, A025591, A077047.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 31 2024