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

%I #13 Jan 30 2024 10:23:10

%S 1,1,4,62,4658,1585430,2319512420,14225426190522,361926393013029354,

%T 37883831957216781279561,16231015449888734994721650504,

%U 28330316118212024049511095643949434,200866780133770636272812495083578779133456,5771133366532656054669819186294860881172794669798

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

%p a:= n-> max(coeffs(expand(mul(1+x^k, k=1..n)^n))):

%p seq(a(n), n=0..14); # _Alois P. Heinz_, Jan 30 2024

%t Table[Max[CoefficientList[Product[(1 + x^k)^n, {k, 1, n}], x]], {n, 0, 13}]

%o (PARI) a(n) = vecmax(Vec(prod(k=1, n, (1+x^k))^n)); \\ _Michel Marcus_, Jan 30 2024

%Y Cf. A025591, A047653, A270913, A369709.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 30 2024