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

%I A119694 #23 Apr 12 2024 06:13:11
%S A119694 0,1,2,10,42,210,1056,5577,30030,165308,923780,5231954,29953728,
%T A119694 173095700,1008263880,5913855450,34898020290,207042729630,
%U A119694 1234218400800,7388927397390,44406274641300,267807758800920,1620247684628040,9831059348368050,59810275503119232
%N A119694 a(n) = Fibonacci(n) * Catalan(n).
%H A119694 Alois P. Heinz, <a href="/A119694/b119694.txt">Table of n, a(n) for n = 0..1000</a>
%F A119694 a(n) = A000045(n) * A000108(n). - _Alois P. Heinz_, Aug 12 2017
%F A119694 Sum_{n>=0} a(n)/8^n = 4 - 6*sqrt(2/5). - _Amiram Eldar_, May 04 2023
%F A119694 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
%p A119694 seq(combinat[fibonacci](n)*(binomial(2*n, n)/(n+1)), n=0..27);
%p A119694 # second Maple program:
%p A119694 a:= proc(n) option remember; `if`(n<2, n,
%p A119694       ((2*n-1)*(2*n*a(n-1)+(8*n-12)*a(n-2)))/(n*(n+1)))
%p A119694     end:
%p A119694 seq(a(n), n=0..25);  # _Alois P. Heinz_, Aug 12 2017
%t A119694 Table[Fibonacci[n]CatalanNumber[n],{n,0,30}] (* _Harvey P. Dale_, Aug 27 2017 *)
%Y A119694 Cf. A000045, A000108, A000984.
%K A119694 easy,nonn
%O A119694 0,3
%A A119694 _Zerinvary Lajos_, Jun 09 2006
%E A119694 Name edited by _Alois P. Heinz_, Aug 12 2017