A369438 a(n) = [x^(n^3)] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

1, 1, 1, 1, 1, 1, 2, 3, 4, 11, 24, 46, 106, 238, 537, 1318, 3007, 7027, 18199, 43202, 105900, 279860, 688474, 1741235, 4641670, 11790546, 30529486, 82306963, 213852619, 563866091, 1531711961, 4047719392, 10835966180, 29624064007, 79423421277, 215083283638

Offset: 0

Author

Ilya Gutkovskiy, Jan 23 2024

Keywords

• nonn

Crossrefs

Cf. A000578, A316706, A368845, A369345.

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(n^3, n):
seq(a(n), n=0..35);  # Alois P. Heinz, Jan 23 2024

Mathematica

Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, n^3], {n, 0, 34}]