%I #11 Aug 05 2023 13:12:10

%S 1,1,0,-3,-3,17,45,-90,-546,130,5832,7074,-53625,-159214,374517,

%T 2419131,-728364,-30011530,-37519884,307731042,940757526,-2343385995,

%U -15421126275,5164279686,203045257272,255851517115,-2186669342070,-6760669947375,17391580425180

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

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

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

%Y Cf. A364735, A364737, A364738.

%Y Cf. A300048.

%K sign

%O 0,4

%A _Seiichi Manyama_, Aug 05 2023