%I #12 Jun 23 2023 10:31:57

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

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

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

%N Expansion of Product_{k>0} (1 - x^(7*k-5)) * (1 - x^(7*k-2)) * (1 - x^(7*k)).

%F G.f.: Sum_{k in Z} (-1)^k * x^(k * (7*k + 3) / 2).

%F a(0) = 1; a(n) = -(1/n) * Sum_{k=1..n} A363803(k) * a(n-k).

%o (PARI) my(N=100, x='x+O('x^N)); Vec(prod(k=1, N, 1-[1, 0, 1, 0, 0, 1, 0][k%7+1]*x^k))

%Y Convolution inverse of A346797.

%Y Cf. A232714, A363801.

%Y Cf. A186029, A218471, A363803.

%K sign

%O 0

%A _Seiichi Manyama_, Jun 23 2023