A359966 - OEIS

%I #12 Jan 21 2023 02:02:03

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

%T 1,0,0,-2,0,0,1,1,0,0,-1,1,0,0,-1,-1,-1,0,2,1,0,-1,0,0,1,0,-1,0,0,1,

%U -1,0,0,0,0,-1,0,0,1,0,1,0,-1,-1,0,1,1,0,-2,-1,1,3

%N Expansion of Product_{k>=2} (1 - x^(k^2-1)) in powers of x.

%H Seiichi Manyama, <a href="/A359966/b359966.txt">Table of n, a(n) for n = 0..10000</a>

%F a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A359967(k) * a(n-k).

%o (PARI) my(N=100, x='x+O('x^N)); Vec(prod(k=2, sqrtint(N+1), 1-x^(k^2-1)))

%o (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 Cf. A005563, A276516, A359936, A359967.

%K sign

%O 0,36

%A _Seiichi Manyama_, Jan 20 2023