A369712 Maximal coefficient of (1 + x) * (1 + x^2)^2 * (1 + x^3)^3 * ... * (1 + x^n)^n.

1, 1, 2, 9, 79, 1702, 78353, 7559080, 1509040932, 619097417818, 519429629728698, 887531129680197018, 3078434842626707386602, 21627792113204714623569767, 307257554772242590850211062866, 8813577747274880345454470354985336, 509819403352972623999938010230619997952

Offset: 0

Author

Ilya Gutkovskiy, Jan 29 2024

Keywords

• nonn

Crossrefs

Cf. A025591, A026007, A047653.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, expand(b(n-1)*(1+x^n)^n)) end:
a:= n-> max(coeffs(b(n))):
seq(a(n), n=0..16);  # Alois P. Heinz, Jan 29 2024

Mathematica

Table[Max[CoefficientList[Product[(1 + x^k)^k, {k, 1, n}], x]], {n, 0, 16}]

PARI

a(n) = vecmax(Vec(prod(k=1, n, (1+x^k)^k))); \\ Michel Marcus, Jan 30 2024