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G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^3.
3

%I #8 Jul 30 2023 09:56:36

%S 1,3,7,19,63,231,895,3615,15055,64111,277791,1220767,5427775,24371199,

%T 110350335,503289727,2309992959,10661634303,49452179455,230391918591,

%U 1077644520703,5058766156543,23824929459711,112541456498175,533063457631231,2531252417738751

%N G.f. satisfies A(x) = 1/(1-x)^3 + x^2*A(x)^3.

%F a(n) = Sum_{k=0..floor(n/2)} binomial(n+4*k+2,6*k+2) * binomial(3*k,k) / (2*k+1).

%o (PARI) a(n) = sum(k=0, n\2, binomial(n+4*k+2, 6*k+2)*binomial(3*k, k)/(2*k+1));

%Y Cf. A364625, A364627.

%Y Cf. A086631.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 30 2023