A371616 G.f. satisfies A(x) = 1 + x / (1 - x*A(x)^3)^3.

1, 1, 3, 15, 82, 495, 3147, 20812, 141621, 985287, 6976369, 50108232, 364202415, 2673756449, 19797659586, 147677816532, 1108711280376, 8371222635096, 63525564996093, 484243596619753, 3706268752629237, 28470703720193010, 219432896755734137

Offset

0,3

Links

Seiichi Manyama, Table of n, a(n) for n = 0..1000

Formula

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

Prog

(PARI) a(n, r=1, s=3, t=0, u=3) = r*sum(k=0, n, binomial(t*k+u*(n-k)+r, k)*binomial(n+(s-1)*k-1, n-k)/(t*k+u*(n-k)+r));

Crossrefs

Cf. A364742, A367242.

Cf. A001764, A365113.

Cf. A002293, A367281.

Sequence in context: A345885 A014276 A006964 * A203507 A192662 A213096

Adjacent sequences: A371613 A371614 A371615 * A371617 A371618 A371619

Keyword

nonn

Author

Seiichi Manyama, Mar 29 2024

Status

approved