|
%I #14 Aug 10 2020 09:26:57
%S 1,-1,-2,-3,-5,-10,-27,-91,-350,-1459,-6466,-30258,-149051,-771157,
%T -4181702,-23718221,-140437759,-866481074,-5561061327,-37066185842,
%U -256190732502,-1833581728979,-13571059095383,-103744579461855,-818183156375886,-6649600332967494,-55635988924348030
%N Expansion of Product_{k>=1} (1 - x^k / (1 - k*x)).
%F G.f.: exp( - Sum_{k>=1} x^k * Sum_{d|k} 1 / (d * (1 - k/d * x)^d)).
%t m = 26; CoefficientList[Series[Product[(1 - x^k/(1 - k*x)), {k, 1, m}], {x, 0, m}], x] (* _Amiram Eldar_, Aug 10 2020 *)
%o (PARI) N=40; x='x+O('x^N); Vec(prod(k=1, N, 1-x^k/(1-k*x)))
%o (PARI) N=40; x='x+O('x^N); Vec(exp(-sum(k=1, N, x^k*sumdiv(k, d, 1/(d*(1-k/d*x)^d)))))
%Y Convolution inverse of A336990.
%Y Cf. A307599, A336989.
%K sign
%O 0,3
%A _Seiichi Manyama_, Aug 10 2020
|
