A119694 a(n) = Fibonacci(n) * Catalan(n).

0, 1, 2, 10, 42, 210, 1056, 5577, 30030, 165308, 923780, 5231954, 29953728, 173095700, 1008263880, 5913855450, 34898020290, 207042729630, 1234218400800, 7388927397390, 44406274641300, 267807758800920, 1620247684628040, 9831059348368050, 59810275503119232

Offset: 0

Author

Zerinvary Lajos, Jun 09 2006

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000045, A000108, A000984.

Programs

Maple

seq(combinat[fibonacci](n)*(binomial(2*n, n)/(n+1)), n=0..27);
# second Maple program:
a:= proc(n) option remember; `if`(n<2, n,
      ((2*n-1)*(2*n*a(n-1)+(8*n-12)*a(n-2)))/(n*(n+1)))
    end:
seq(a(n), n=0..25);  # Alois P. Heinz, Aug 12 2017

Mathematica

Table[Fibonacci[n]CatalanNumber[n],{n,0,30}] (* Harvey P. Dale, Aug 27 2017 *)

Formula

a(n) = A000045(n) * A000108(n). - Alois P. Heinz, Aug 12 2017

Sum_{n>=0} a(n)/8^n = 4 - 6*sqrt(2/5). - Amiram Eldar, May 04 2023

G.f.: (1-sqrt((20*x+4*sqrt(-16*x^2-4*x+1)-12*x+6)/10))/(2*x). - Vladimir Kruchinin, Apr 12 2024

Extensions

Name edited by Alois P. Heinz, Aug 12 2017