A306565 - OEIS

%I #66 May 14 2021 02:53:52

%S 1,-1,-2,-1,1,3,4,3,1,-2,-6,-8,-8,-8,-5,2,8,12,17,22,23,17,7,0,-7,-22,

%T -40,-51,-53,-49,-45,-42,-30,-4,30,65,90,100,112,137,157,152,120,71,

%U 18,-33,-80,-125,-187,-275,-357,-401,-407,-380,-327,-269,-221,-171,-75,102,322,515,669,801

%N Expansion of Product_{k>=1} (1 - x^k * (1 + x)).

%H Seiichi Manyama, <a href="/A306565/b306565.txt">Table of n, a(n) for n = 0..1000</a>

%F G.f.: exp( - Sum_{k>=1} x^k * Sum_{d|k} (1+x)^d / d).

%t m = 63; CoefficientList[Series[Product[1 - x^k * (1 + x), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, May 14 2021 *)

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

%o (PARI) N=66; x='x+O('x^N); Vec(exp(-sum(k=1, N, x^k*sumdiv(k, d, (1+x)^d/d))))

%Y Convolution inverse of A227681.

%Y Cf. A160571.

%K sign

%O 0,3

%A _Seiichi Manyama_, Apr 16 2019