A327758 - OEIS

%I #23 Feb 16 2025 08:33:58

%S 1,1,0,0,1,0,-1,-1,-1,-1,0,1,1,2,3,2,1,0,-2,-4,-4,-4,-3,0,3,5,6,7,4,0,

%T -4,-8,-12,-11,-6,-2,4,12,17,16,12,4,-8,-17,-22,-24,-20,-6,11,24,34,

%U 36,29,12,-10,-33,-47,-50,-40,-18,13,44,66,72,59,27,-16,-58,-89,-100,-84,-41

%N Expansion of Product_{k>=1} 1/(1 - x^k)^(3/k), where (m/n) is the Kronecker symbol.

%H Seiichi Manyama, <a href="/A327758/b327758.txt">Table of n, a(n) for n = 0..1000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KroneckerSymbol.html">Kronecker Symbol</a>

%o (PARI) N=66; x='x+O('x^N); Vec(1/prod(k=1, N, (1-x^k)^kronecker(3, k)))

%Y Convolution inverse of A327757.

%Y Product_{k>=1} 1/(1 - x^k)^(b/k): A111374 (b=2), A000009 (b=4), A003823 (b=5), A214157 (b=13).

%Y Cf. A091338,

%K sign,look,changed

%O 0,14

%A _Seiichi Manyama_, Sep 24 2019