A369706 Maximal coefficient of (1 + x^2) * (1 + x^3) * (1 + x^4) * ... * (1 + x^n).

1, 1, 1, 1, 1, 2, 3, 4, 7, 12, 20, 35, 62, 112, 199, 361, 657, 1206, 2221, 4110, 7636, 14234, 26618, 49910, 93846, 176906, 334184, 632602, 1199892, 2280164, 4340064, 8273610, 15796439, 30202620, 57820648, 110826888, 212681976, 408610024, 785833480, 1512776590, 2915017360

Offset

0,6

Links

Table of n, a(n) for n=0..40.

Formula

a(n) ~ A025591(n)/2. - Vaclav Kotesovec, Jan 29 2024

Maple

b:= proc(n) option remember; `if`(n<2, 1, expand(b(n-1)*(1+x^n))) end:
a:= n-> max(coeffs(b(n))):
seq(a(n), n=0..40);  # Alois P. Heinz, Jan 29 2024

Mathematica

Table[Max[CoefficientList[Product[(1 + x^k), {k, 2, n}], x]], {n, 0, 40}]

Prog

(PARI) a(n) = vecmax(Vec(prod(i=2, n, 1+x^i))); \\ Michel Marcus, Jan 29 2024

Crossrefs

Cf. A025147, A025591.

Sequence in context: A357532 A018148 A084972 * A307673 A141002 A006537

Adjacent sequences: A369703 A369704 A369705 * A369707 A369708 A369709

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 29 2024

Status

approved