A071727 Expansion of (1+x^3*C)*C^2, where C = (1-(1-4*x)^(1/2))/(2*x) is g.f. for Catalan numbers, A000108.

1, 2, 5, 15, 45, 141, 457, 1520, 5159, 17797, 62218, 219946, 784890, 2823666, 10229733, 37289210, 136665195, 503301525, 1861550310, 6912114330, 25755891510, 96279420870, 360961760250, 1356920443944, 5113523451462, 19314197605826, 73105593170132, 277253358421060

Offset

0,2

Links

Table of n, a(n) for n=0..27.

Formula

For n > 0, a(n) = 3*binomial(2*n-4,n-3)/n+2*binomial(2*n+1,n)/(n+2). - Tani Akinari, Nov 28 2024

Maple

a:= proc(n) option remember; `if`(n<3, 1+n^2,
      2*(2*n-5)*(67*n^3-93*n^2-28*n+12)*a(n-1)/
        ((n+2)*(67*n^3-294*n^2+359*n-120)))
    end:
seq(a(n), n=0..27);  # Alois P. Heinz, Nov 28 2024

Prog

(Maxima) a(n):=if n=0 then 1 else 3*binomial(2*n-4, n-3)/n+2*binomial(2*n+1, n)/(n+2);
makelist(a(n), n, 0, 50); /* Tani Akinari, Nov 28 2024 */

Crossrefs

Cf. A000108.

Sequence in context: A232208 A294502 A254534 * A148354 A364330 A151279

Adjacent sequences: A071724 A071725 A071726 * A071728 A071729 A071730

Keyword

nonn

Author

N. J. A. Sloane, Jun 06 2002

Status

approved