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A359936 Expansion of Product_{k>=0} (1 - x^(k^2+1)) in powers of x.

%I A359936 #14 Jan 19 2023 09:34:32
%S A359936 1,-1,-1,1,0,-1,1,1,-1,0,-1,1,1,-1,0,1,-1,-2,2,1,-1,0,1,-1,-1,1,-1,2,
%T A359936 0,-2,1,1,-2,0,2,-1,1,-2,0,2,-1,-1,2,1,-3,0,1,1,-2,0,1,0,0,-1,3,0,-3,
%U A359936 0,2,-2,1,1,-2,2,-2,-2,4,2,-4,1,2,-3,-1,1,2,1,-1,-3,2
%N A359936 Expansion of Product_{k>=0} (1 - x^(k^2+1)) in powers of x.
%H A359936 Seiichi Manyama, <a href="/A359936/b359936.txt">Table of n, a(n) for n = 0..10000</a>
%F A359936 a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A359937(k) * a(n-k).
%o A359936 (PARI) my(N=100, x='x+O('x^N)); Vec(prod(k=0, sqrtint(N), 1-x^(k^2+1)))
%o A359936 (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-1)*d)*v[i-j+1])/i); v;
%Y A359936 Cf. A002522, A081362, A276516, A284312, A284313, A284314, A284585, A284499, A357911, A359937.
%K A359936 sign,look
%O A359936 0,18
%A A359936 _Seiichi Manyama_, Jan 19 2023