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G.f. satisfies A(x) = 1 + x/(1 + x^3)^2 * A(x/(1 + x^3)).
3

%I #12 Feb 26 2023 06:56:13

%S 1,1,1,1,-1,-4,-8,-10,2,40,115,174,22,-736,-2495,-4276,-920,20593,

%T 75011,135814,17524,-788871,-2909061,-5248648,623274,38581252,

%U 138036877,235567666,-134440249,-2284840691,-7698637124,-11745925435,15869626983,157479613343

%N G.f. satisfies A(x) = 1 + x/(1 + x^3)^2 * A(x/(1 + x^3)).

%H Seiichi Manyama, <a href="/A360900/b360900.txt">Table of n, a(n) for n = 0..1000</a>

%F a(0) = 1; a(n) = Sum_{k=0..floor((n-1)/3)} (-1)^k * binomial(n-2*k,k) * a(n-1-3*k).

%o (PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, (i-1)\3, (-1)^j*binomial(i-2*j, j)*v[i-3*j])); v;

%Y Cf. A352865, A360901.

%Y Cf. A360892.

%K sign

%O 0,6

%A _Seiichi Manyama_, Feb 25 2023