A369705 Maximal coefficient of (1 + x) * (1 - x^2) * (1 + x^3) * ... * (1 - (-x)^n).

1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 3, 2, 2, 3, 3, 4, 6, 5, 6, 7, 7, 8, 10, 11, 16, 16, 19, 21, 23, 28, 34, 41, 50, 56, 68, 80, 91, 110, 135, 158, 196, 225, 269, 320, 376, 447, 544, 644, 786, 921, 1111, 1321, 1573, 1882, 2274, 2711, 3280, 3895, 4694, 5591, 6718

Offset: 0

Author

Ilya Gutkovskiy, Jan 29 2024

Keywords

• nonn

Crossrefs

Cf. A025591, A039828, A086376, A121373.

Programs

Maple

b:= proc(n) option remember; `if`(n=0, 1, expand(b(n-1)*(1-(-x)^n))) end:
a:= n-> max(coeffs(b(n))):
seq(a(n), n=0..60);  # Alois P. Heinz, Jan 29 2024

Mathematica

Table[Max[CoefficientList[Product[(1 - (-x)^k), {k, 1, n}], x]], {n, 0, 60}]

PARI

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