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a(1) = a(2) = 1; a(n+1) = -Sum_{d|n, d < n} a(n/d) * a(d).
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%I #6 Feb 17 2021 20:29:43

%S 1,1,-1,1,-2,2,0,0,-2,1,3,-3,1,-1,1,-5,4,-4,12,-12,14,-14,8,-8,10,-14,

%T 12,-16,18,-18,26,-26,36,-30,22,-22,24,-24,0,2,20,-20,-10,10,12,-18,2,

%U -2,14,-14,-2,10,16,-16,-8,20,14,10,-46,46,-52,52,-104,132,-70,74,-186,186,-134,150

%N a(1) = a(2) = 1; a(n+1) = -Sum_{d|n, d < n} a(n/d) * a(d).

%t a[1] = a[2] = 1; a[n_] := a[n] = -Sum[If[d < (n - 1), a[(n - 1)/d] a[d], 0], {d, Divisors[n - 1]}]; Table[a[n], {n, 70}]

%o (PARI) A341698(n) = if(n<3, 1, sumdiv(n-1,d,if(d<(n-1), -A341698((n-1)/d)*A341698(d), 0))); \\ _Antti Karttunen_, Feb 17 2021

%Y Cf. A038044, A325303, A341697.

%K sign

%O 1,5

%A _Ilya Gutkovskiy_, Feb 17 2021