A369725 Maximal coefficient of ( (1 + x) * (1 + x^2) * (1 + x^3) * ... * (1 + x^n) )^n.

1, 1, 4, 62, 4658, 1585430, 2319512420, 14225426190522, 361926393013029354, 37883831957216781279561, 16231015449888734994721650504, 28330316118212024049511095643949434, 200866780133770636272812495083578779133456, 5771133366532656054669819186294860881172794669798

Offset

0,3

Links

Table of n, a(n) for n=0..13.

Maple

a:= n-> max(coeffs(expand(mul(1+x^k, k=1..n)^n))):
seq(a(n), n=0..14);  # Alois P. Heinz, Jan 30 2024

Mathematica

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

Prog

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

Crossrefs

Cf. A025591, A047653, A270913, A369709.

Sequence in context: A191300 A087613 A350282 * A284158 A202630 A102196

Adjacent sequences: A369722 A369723 A369724 * A369726 A369727 A369728

Keyword

nonn

Author

Ilya Gutkovskiy, Jan 30 2024

Status

approved