Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #6 Mar 23 2019 12:39:01
%S 1,1,0,-2,-2,0,4,4,-2,-10,-6,10,22,4,-34,-46,16,102,86,-100,-272,-126,
%T 370,650,60,-1138,-1384,526,3142,2532,-2936,-7952,-3440,10802,18426,
%U 596,-33344,-38418,18716,91934,68400,-93402,-230962,-86236,330144,528880,-17298,-996040
%N Expansion of 1/(1 - Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).
%C Invert transform of A008836.
%F a(0) = 1; a(n) = Sum_{k=1..n} A008836(k)*a(n-k).
%t nmax = 47; CoefficientList[Series[1/(1 - Sum[LiouvilleLambda[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
%t a[0] = 1; a[n_] := a[n] = Sum[LiouvilleLambda[k] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 47}]
%Y Cf. A008836, A118206, A118207, A300663.
%K sign
%O 0,4
%A _Ilya Gutkovskiy_, Mar 22 2019