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

%I #12 Jan 24 2024 14:16:32

%S 1,1,0,0,0,0,0,4,6,15,24,40,69,138,396,1028,3062,8269,21680,50955,

%T 115457,262239,631393,1666438,4558051,12913587,35530351,95825467,

%U 246943968,628040166,1607703060,4228528070,11485131123,31616483271,88141192570,243487667830

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

%H Vaclav Kotesovec, <a href="/A369437/b369437.txt">Table of n, a(n) for n = 0..108</a>

%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$2):

%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], {n, 0, 34}]

%Y Cf. A000578, A316706, A348892, A369345.

%K nonn

%O 0,8

%A _Ilya Gutkovskiy_, Jan 23 2024