A367062 - OEIS

%I #10 Nov 04 2023 10:11:58

%S 1,1,3,13,64,339,1889,10917,64836,393292,2426335,15176847,96029114,

%T 613540477,3952727925,25649572693,167494312692,1099850119488,

%U 7257905610260,48106858236044,320131295055690,2138010763838375,14325505944147495,96273042489762471

%N G.f. satisfies A(x) = 1 + x*A(x)^3 + x^3*A(x)^6.

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

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

%Y Cf. A366676, A367057, A367058, A367059, A367060, A367061.

%K nonn

%O 0,3

%A _Seiichi Manyama_, Nov 04 2023