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Expansion of Product_{k>0} (1 - x^(3*k)) / (1 - x^(3*k - 1)).
2

%I #7 Apr 08 2017 09:50:17

%S 1,0,1,-1,1,0,0,0,0,0,1,-1,1,-1,0,1,0,0,0,-1,1,0,0,0,0,0,1,-1,0,0,0,0,

%T 1,-1,1,0,-1,1,-1,0,1,-1,1,0,0,0,0,-1,1,0,0,0,0,-1,1,0,0,1,-1,0,1,-1,

%U 0,0,-1,1,1,-1,1,-1,0,1,0,-1,1,-1,0,1,-1,0,1,-1,1,0,-1,1,0,-1,1,0,0,0,0,-1,1,0,-1,1,-1,0,2,-1,0,1,-1

%N Expansion of Product_{k>0} (1 - x^(3*k)) / (1 - x^(3*k - 1)).

%C |a(n)|<2 if n<100, |a(n)|<3 if n<175.

%H Seiichi Manyama, <a href="/A143240/b143240.txt">Table of n, a(n) for n = 0..10000</a>

%F Euler transform of period 3 sequence [ 0, 1, -1, ...].

%F G.f.: Product_{k>0} (1 - x^(3*k)) / (1 - x^(3*k - 1)).

%e 1 + q^2 - q^3 + q^4 + q^10 - q^11 + q^12 - q^13 + q^15 - q^19 + q^20 + ...

%o (PARI) {a(n) = if( n<0, 0, polcoeff( prod(k=1, (n+1)\3, (1 - x^(3*k)) / (1 - x^(3*k - 1)), 1 + x * O(x^n)), n))}

%Y Cf. A113706.

%K sign

%O 0,101

%A _Michael Somos_, Aug 01 2008