A364622 G.f. satisfies A(x) = 1/(1-x)^2 + x^2*A(x)^4.

1, 2, 4, 12, 45, 182, 779, 3480, 16005, 75234, 359893, 1746268, 8573477, 42511646, 212587561, 1070897000, 5429174465, 27679933778, 141829437174, 729972918876, 3772160853821, 19563615260102, 101797930474515, 531293155760840, 2780515192595481, 14588670579665882

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Formula

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

Mathematica

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 *)

Prog

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

Crossrefs

Cf. A086615, A086631.

Sequence in context: A238111 A165901 A074449 * A359328 A332235 A131387

Adjacent sequences: A364619 A364620 A364621 * A364623 A364624 A364625

Keyword

nonn

Author

Seiichi Manyama, Jul 30 2023

Status

approved