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G.f. A(x) satisfies A(x) = 1 + x + x^3*A(x)^3.
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%I #11 Oct 14 2023 13:59:49

%S 1,1,0,1,3,3,4,15,30,42,99,255,475,915,2232,4977,9945,21945,51093,

%T 110634,238005,542341,1227390,2696841,6035886,13770402,31001133,

%U 69485295,157945293,359888373,814699002,1850816823,4231092060,9659302380,22028018679

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

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

%F a(n) = A366591(n) + A366591(n-1).

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

%Y Cf. A019497, A366266, A366556.

%Y Cf. A366591.

%K nonn

%O 0,5

%A _Seiichi Manyama_, Oct 13 2023