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a(1) = 1; a(n+1) = -a(n) + 2 * Sum_{d|n} a(n/d) * a(d).
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%I #5 Feb 20 2022 06:45:41

%S 1,1,3,9,29,87,273,819,2493,7497,22607,67821,203919,611757,1836363,

%T 5509437,16531749,49595247,148796757,446390271,1339201845,4017608811,

%U 12052916861,36158750583,108476535993,325429609661,976289644659,2928868963893,8786609348535

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

%F G.f.: x * ( 1 + 2 * Sum_{i>=1} Sum_{j>=2} a(i) * a(j) * x^(i*j) ) / (1 - x).

%F a(n) = A351787(n) / 2 for n > 1.

%t a[1] = 1; a[n_] := a[n] = -a[n - 1] + 2 Sum[a[(n - 1)/d] a[d], {d, Divisors[n - 1]}]; Table[a[n], {n, 1, 29}]

%Y Cf. A038044, A084978, A122698, A277120, A339755, A341697, A345139, A351787, A351788.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, Feb 19 2022