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%I #10 Sep 17 2023 10:00:00
%S 1,0,0,0,1,1,0,0,3,7,4,0,12,45,55,22,55,286,546,455,413,1820,4760,
%T 6120,5304,12597,38760,67830,73587,108262,309925,672980,928763,
%U 1171390,2598310,6270030,10607025,14033565,24293880,57256875,112293597,167416275,255805056
%N G.f. satisfies A(x) = 1 + x^4*A(x)^3*(1 + x*A(x)).
%F a(n) = Sum_{k=0..floor(n/4)} binomial(k,n-4*k) * binomial(n-k+1,k) / (n-k+1).
%o (PARI) a(n) = sum(k=0, n\4, binomial(k, n-4*k)*binomial(n-k+1, k)/(n-k+1));
%Y Cf. A365727, A365728, A365730, A365731.
%Y Cf. A365697.
%K nonn
%O 0,9
%A _Seiichi Manyama_, Sep 17 2023
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