login
Maximal coefficient of (1 - x) * (1 - x^2)^2 * (1 - x^3)^3 * ... * (1 - x^n)^n.
0

%I #13 Jan 30 2024 12:06:14

%S 1,1,2,5,30,289,5170,155768,7947236,695357704,105014923458,

%T 26823702973095,12124672181643014,9302296598744837059,

%U 12142590791028740988194,26874517085010633423659616,100413718348008543669377307304,634527279123990475683817934978079

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

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

%p seq(a(n), n=0..17); # _Alois P. Heinz_, Jan 30 2024

%t Table[Max[CoefficientList[Product[(1 - x^k)^k, {k, 1, n}], x]], {n, 0, 17}]

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

%Y Cf. A073592, A086376, A369710, A369711, A369712.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Jan 30 2024