A367056 G.f. satisfies A(x) = 1 + x*A(x)^2 + x^3*A(x).

1, 1, 2, 6, 17, 52, 168, 561, 1922, 6719, 23871, 85938, 312823, 1149421, 4257460, 15880036, 59594517, 224856450, 852491806, 3245959002, 12407332166, 47592364107, 183139542306, 706794663136, 2735053815771, 10609811267757, 41251228784198

Offset: 0

Author

Seiichi Manyama, Nov 04 2023

Keywords

• nonn

Crossrefs

Cf. A049140, A071969, A125305, A216490, A367042.

Programs

Maple

A367056 := proc(n)
    add(binomial(n-2*k+1,k) * binomial(2*n-5*k,n-3*k)/(n-2*k+1),k=0..floor(n/3)) ;
end proc:
seq(A367056(n),n=0..70) ; # R. J. Mathar, Dec 04 2023

PARI

a(n) = sum(k=0, n\3, binomial(n-2*k+1, k)*binomial(2*n-5*k, n-3*k)/(n-2*k+1));

Formula

G.f.: A(x) = 2 / (1-x^3+sqrt((1-x^3)^2-4*x)).

a(n) = Sum_{k=0..floor(n/3)} binomial(n-2*k+1,k) * binomial(2*n-5*k,n-3*k)/(n-2*k+1).

D-finite with recurrence (n+1)*a(n) +2*(-2*n+1)*a(n-1) +(-2*n+7)*a(n-3) +(n-8)*a(n-6)=0. - R. J. Mathar, Dec 04 2023