A367073 - OEIS

%I #10 Nov 05 2023 09:01:24

%S 1,2,0,1,6,12,11,30,120,252,408,1104,3415,7710,15984,42609,118422,

%T 281820,657468,1732008,4608288,11375240,28100400,73598112,192776895,

%U 487507038,1239516384,3241480275,8460205842,21733941060,56121723411,146904032622,383900676120

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

%F a(n) = Sum_{k=0..floor(n/3)} 2^(n-3*k) * binomial(2*k+1,n-3*k) * A001764(k).

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

%Y Cf. A001764, A366555, A367072, A367074.

%Y Cf. A367112.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Nov 05 2023