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%I #23 Oct 23 2022 23:59:37
%S 1,-1,2,-2,2,0,-4,12,-22,34,-42,38,-6,-68,202,-394,616,-782,730,-204,
%T -1104,3486,-6994,11142,-14452,14026,-5296,-17558,60042,-123860,
%U 201128,-266384,268176,-124034,-273626,1030396,-2188864,3624290,-4898740,5101306,-2744408
%N Expansion of 1 / (1 + Sum_{k>=1} lambda(k)*x^k), where lambda() is the Liouville function (A008836).
%F a(0) = 1; a(n) = -Sum_{k=1..n} A008836(k) * a(n-k).
%t nmax = 40; 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, 40}]
%Y Cf. A008836, A118205, A118206, A118207, A118208, A185694, A307076, A307240.
%K sign
%O 0,3
%A _Ilya Gutkovskiy_, Oct 02 2022
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