A367112 - OEIS

%I #9 Nov 05 2023 09:01:12

%S 1,2,4,9,24,72,227,730,2384,7916,26704,91280,315319,1098710,3856948,

%T 13628441,48435808,173030048,620965396,2237681720,8093572960,

%U 29372735368,106925552672,390336084256,1428620011263,5241166583502,19270575881964

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

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

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

%Y Cf. A001764, A071879, A367111, A367113.

%Y Cf. A367073.

%K nonn,easy

%O 0,2

%A _Seiichi Manyama_, Nov 05 2023