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A369437 a(n) = [x^n] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).

%I A369437 #12 Jan 24 2024 14:16:32
%S A369437 1,1,0,0,0,0,0,4,6,15,24,40,69,138,396,1028,3062,8269,21680,50955,
%T A369437 115457,262239,631393,1666438,4558051,12913587,35530351,95825467,
%U A369437 246943968,628040166,1607703060,4228528070,11485131123,31616483271,88141192570,243487667830
%N A369437 a(n) = [x^n] Product_{k=1..n} (x^(k^3) + 1 + 1/x^(k^3)).
%H A369437 Vaclav Kotesovec, <a href="/A369437/b369437.txt">Table of n, a(n) for n = 0..108</a>
%p A369437 b:= proc(n, i) option remember; `if`(n>(i*(i+1)/2)^2, 0,
%p A369437      `if`(i=0, 1, b(n, i-1)+b(n+i^3, i-1)+b(abs(n-i^3), i-1)))
%p A369437     end:
%p A369437 a:= n-> b(n$2):
%p A369437 seq(a(n), n=0..35);  # _Alois P. Heinz_, Jan 23 2024
%t A369437 Table[Coefficient[Product[(x^(k^3) + 1 + 1/x^(k^3)), {k, 1, n}], x, n], {n, 0, 34}]
%Y A369437 Cf. A000578, A316706, A348892, A369345.
%K A369437 nonn
%O A369437 0,8
%A A369437 _Ilya Gutkovskiy_, Jan 23 2024