A369345 a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

1, 1, 1, 1, 1, 1, 3, 3, 5, 17, 31, 61, 139, 309, 701, 1651, 3849, 8929, 22295, 53777, 131025, 335619, 837999, 2107947, 5484373, 14071891, 36275323, 95881995, 250956301, 659257445, 1763642977, 4685724391, 12496708267, 33766814039, 90846586161, 245197523769

Offset: 0

Author

Ilya Gutkovskiy, Jan 20 2024

Keywords

• nonn

Comments

All terms are odd.

Crossrefs

Cf. A000578, A007576, A158118, A350249.

Programs

Maple

b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
     `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
    end:
a:= n-> b(0, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 21 2024

Mathematica

Table[Coefficient[Product[x^(k^3) + 1 + 1/x^(k^3), {k, 1, n}], x, 0], {n, 0, 33}]