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a(0) = 1; a(n) = Sum_{k=1..n} -lambda(k+1)*a(n-k), where lambda() is the Liouville function (A008836).
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%I #5 Mar 30 2019 08:39:11

%S 1,1,2,2,4,4,8,10,18,22,38,50,84,114,186,256,406,570,896,1280,1986,

%T 2862,4394,6380,9730,14224,21582,31690,47872,70544,106248,157016,

%U 235930,349382,523976,777144,1163882,1728396,2585802,3843568,5745510,8546218,12767232,19001168

%N a(0) = 1; a(n) = Sum_{k=1..n} -lambda(k+1)*a(n-k), where lambda() is the Liouville function (A008836).

%F G.f.: x / Sum_{k>=1} lambda(k)*x^k.

%t a[0] = 1; a[n_] := a[n] = Sum[-LiouvilleLambda[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 43}]

%t nmax = 43; CoefficientList[Series[x/Sum[LiouvilleLambda[k] x^k, {k, 1, nmax + 1}], {x, 0, nmax}], x]

%Y Cf. A008836, A073776, A307076.

%K nonn

%O 0,3

%A _Ilya Gutkovskiy_, Mar 30 2019