A364622 - OEIS

%I #9 Jan 20 2024 14:44:56

%S 1,2,4,12,45,182,779,3480,16005,75234,359893,1746268,8573477,42511646,

%T 212587561,1070897000,5429174465,27679933778,141829437174,

%U 729972918876,3772160853821,19563615260102,101797930474515,531293155760840,2780515192595481,14588670579665882

%N G.f. satisfies A(x) = 1/(1-x)^2 + x^2*A(x)^4.

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

%t Table[Sum[Binomial[n + 4 k + 1, 6 k + 1]*Binomial[4 k, k]/(3 k + 1), {k, 0, Floor[n/2]}], {n, 0, 30}] (* _Wesley Ivan Hurt_, Jan 20 2024 *)

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

%Y Cf. A086615, A086631.

%K nonn

%O 0,2

%A _Seiichi Manyama_, Jul 30 2023