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

%I #10 Oct 18 2023 09:58:37

%S 1,4,5,15,-5,111,-402,2172,-10892,57362,-305756,1656560,-9083341,

%T 50328219,-281324174,1584578882,-8984740332,51242962422,-293772467974,

%U 1691974930794,-9785378133066,56805049768410,-330880419984556,1933299689139664,-11328101469158229

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

%F G.f.: A(x) = -2*x / (1-sqrt(1+4*x*(1-x)^3)).

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

%o (PARI) a(n) = (-1)^(n-1)*sum(k=0, n, binomial(2*k-1, k)*binomial(3*(k-1), n-k)/(2*k-1));

%Y Cf. A366363, A363816.

%K sign

%O 0,2

%A _Seiichi Manyama_, Oct 18 2023