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%I #10 Sep 16 2023 10:42:48
%S 1,0,0,1,1,1,6,12,19,62,156,318,852,2254,5262,13441,35543,88772,
%T 226880,596937,1539188,3980364,10468270,27410289,71702956,189169352,
%U 499529048,1318355542,3493861461,9278408639,24647900618,65620808508,175037591303,467277998136
%N G.f. satisfies A(x) = 1 + x^3*A(x)^5 / (1 - x*A(x)).
%F a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k-1,n-3*k) * binomial(n+2*k+1,k) / (n+2*k+1).
%o (PARI) a(n) = sum(k=0, n\3, binomial(n-2*k-1, n-3*k)*binomial(n+2*k+1, k)/(n+2*k+1));
%Y Cf. A023426, A023432, A054514, A114997, A365694.
%K nonn
%O 0,7
%A _Seiichi Manyama_, Sep 16 2023
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