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%I #6 Jun 27 2024 06:26:53
%S 1,-1,0,-1,0,1,-1,1,0,0,1,0,-1,1,-1,1,0,-1,0,0,-1,1,0,-1,1,-1,0,1,-1,
%T 0,1,-1,1,1,-1,0,0,-1,2,0,-1,1,0,-1,2,-2,0,1,-1,0,1,-1,0,1,-2,1,1,-2,
%U 1,0,-2,2,0,-2,2,-1,0,2,-1,-1,1,-1,-1,3,-2,0,2,-2,1,2,-3,1,1,-2,2,1
%N Expansion of Product_{k>=1} (1 - x^(3*k-2)) * (1 - x^(3*k)).
%H Ilya Gutkovskiy, <a href="/A374058/a374058.jpg">Scatterplot of a(n) up to n=10000</a>
%F a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A082051(k) * a(n-k).
%F a(0) = 1; a(n) = -Sum_{k=1..n} A035360(k) * a(n-k).
%F a(n) = Sum_{k=0..n} A010815(k) * A035386(n-k).
%t nmax = 85; CoefficientList[Series[Product[(1 - x^(3 k - 2)) (1 - x^(3 k)), {k, 1, nmax}], {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = -(1/n) Sum[Plus @@ Select[Divisors[k], Mod[#, 3] != 2 &] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 85}]
%Y Cf. A010815, A035360, A035386, A081362, A082051, A132463, A137569, A274719, A284312, A374060.
%K sign
%O 0,39
%A _Ilya Gutkovskiy_, Jun 27 2024
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