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G.f. satisfies A(x) = 1 + x * (1 + x^2)^2 * A(x * (1 + x^2)).
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%I #8 Feb 25 2023 08:41:02

%S 1,1,1,3,6,11,29,71,179,505,1405,4128,12639,39268,127059,420281,

%T 1423787,4955200,17579398,63796635,236161396,890544028,3422553065,

%U 13377869976,53184706291,214870633711,881485304157,3671033616614,15507956547021,66429816610908

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

%F a(0) = 1; a(n) = Sum_{k=0..floor(n-1)/2} binomial(n+1-2*k,k) * a(n-1-2*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)\2, binomial(i+1-2*j, j)*v[i-2*j])); v;

%Y Cf. A360887, A360889.

%Y Cf. A360885.

%K nonn

%O 0,4

%A _Seiichi Manyama_, Feb 25 2023