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G.f. satisfies A(x) = 1 + x^2*A(x)^4 / (1 - x*A(x)).
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%I #10 Sep 16 2023 10:41:27

%S 1,0,1,1,5,10,38,101,353,1070,3659,11843,40505,135873,468104,1604375,

%T 5576315,19386656,67950717,238676813,842797959,2983745508,10603445402,

%U 37777263153,134985354179,483438728094,1735527037388,6243193190117,22503637842423

%N G.f. satisfies A(x) = 1 + x^2*A(x)^4 / (1 - x*A(x)).

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

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

%Y Cf. A004148, A005043, A025246, A046736, A365691.

%Y Cf. A365692.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Sep 16 2023