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

%I A369345 #13 Jan 22 2024 01:50:08
%S A369345 1,1,1,1,1,1,3,3,5,17,31,61,139,309,701,1651,3849,8929,22295,53777,
%T A369345 131025,335619,837999,2107947,5484373,14071891,36275323,95881995,
%U A369345 250956301,659257445,1763642977,4685724391,12496708267,33766814039,90846586161,245197523769
%N A369345 a(n) is the constant term in expansion of Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).
%C A369345 All terms are odd.
%p A369345 b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
%p A369345      `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
%p A369345     end:
%p A369345 a:= n-> b(0, n):
%p A369345 seq(a(n), n=0..35);  # _Alois P. Heinz_, Jan 21 2024
%t A369345 Table[Coefficient[Product[x^(k^3) + 1 + 1/x^(k^3), {k, 1, n}], x, 0], {n, 0, 33}]
%Y A369345 Cf. A000578, A007576, A158118, A350249.
%K A369345 nonn
%O A369345 0,7
%A A369345 _Ilya Gutkovskiy_, Jan 20 2024