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A119694
a(n) = Fibonacci(n) * Catalan(n).
5
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
0,3
LINKS
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
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 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
_Zerinvary Lajos_, Jun 09 2006
EXTENSIONS
Name edited by _Alois P. Heinz_, Aug 12 2017
STATUS
approved