|
|
A119694
|
|
a(n) = Fibonacci(n) * Catalan(n).
|
|
3
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
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
|
|
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:
|
|
MATHEMATICA
|
Table[Fibonacci[n]CatalanNumber[n], {n, 0, 30}] (* Harvey P. Dale, Aug 27 2017 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn,changed
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|