%I #9 Jan 24 2024 12:17:28

%S 1,1,1,1,1,1,2,3,4,11,24,46,106,238,537,1318,3007,7027,18199,43202,

%T 105900,279860,688474,1741235,4641670,11790546,30529486,82306963,

%U 213852619,563866091,1531711961,4047719392,10835966180,29624064007,79423421277,215083283638

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

%p b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,

%p `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))

%p end:

%p a:= n-> b(n^3, n):

%p seq(a(n), n=0..35); # _Alois P. Heinz_, Jan 23 2024

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

%Y Cf. A000578, A316706, A368845, A369345.

%K nonn

%O 0,7

%A _Ilya Gutkovskiy_, Jan 23 2024