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A360001 Expansion of Product_{k>=0} (1 - x^(k^2+4)) in powers of x.

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%I A360001 #10 Jan 21 2023 11:51:43
%S A360001 1,0,0,0,-1,-1,0,0,-1,1,0,0,1,0,0,0,0,0,1,0,-1,1,-1,0,1,0,-1,0,1,-2,1,
%T A360001 0,-1,1,1,0,0,1,-2,0,-1,-2,1,0,1,2,1,-1,1,0,-2,1,-1,-2,0,1,0,0,1,-1,1,
%U A360001 1,0,0,-1,-1,1,1,-2,2,0,-2,2,1,-3,0,1,-3,2,2,-1,1
%N A360001 Expansion of Product_{k>=0} (1 - x^(k^2+4)) in powers of x.
%H A360001 Seiichi Manyama, <a href="/A360001/b360001.txt">Table of n, a(n) for n = 0..10000</a>
%o A360001 (PARI) my(N=100, x='x+O('x^N)); Vec(prod(k=0, sqrtint(N), 1-x^(k^2+4)))
%o A360001 (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-sum(j=1, i, sumdiv(j, d, issquare(d-4)*d)*v[i-j+1])/i); v;
%Y A360001 Cf. A276516, A359936, A359966, A359980, A360002, A360003.
%K A360001 sign,look
%O A360001 0,30
%A A360001 _Seiichi Manyama_, Jan 21 2023