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%I #27 Sep 08 2022 08:45:06
%S 1,1,3,12,84,924,16632,482328,22669416,1722875616,211913700768,
%T 42170826452832,13579006117811904,7074662187380001984,
%U 5963940223961341672512,8134814465483270041306368
%N One half of product of first n+1 Lucas numbers A000032.
%H Vincenzo Librandi, <a href="/A070825/b070825.txt">Table of n, a(n) for n = 0..90</a>
%H R. Grünwald, E. Heidel, A. Strätz, M. Sünkel and R. Terbach, <a href="http://www.cogsys.wiai.uni-bamberg.de/teaching/ss12/ba_pj/project_report.pdf">Induction on Number Series</a>, Fakultät fur Wirtschaftsinformatik und Angewandte Informatik, Otto-Friedrich-Universität Bamberg, 2012. - _N. J. A. Sloane_, Feb 07 2013
%F a(n) = (Product_{k=0..n} L(n))/2 with L(n) := A000032(n).
%F Sum_{n>=0} 1/a(n) = 1 + A101690. - _Amiram Eldar_, Nov 09 2020
%t FoldList[Times, LucasL[Range[0, 20]]]/2 (* or *)
%t Table[Round[GoldenRatio^(n(n+1)/2) QPochhammer[-1, GoldenRatio-2, n+1]]/2, {n, 0, 20}] (* _Vladimir Reshetnikov_, Sep 15 2016 *)
%o (PARI) a(n) = prod(k=0, n, fibonacci(k+1)+fibonacci(k-1))/2; \\ _Michel Marcus_, Mar 18 2016
%o (Magma) [1] cat [&*[Lucas(i+1): i in [0..n]]: n in [0..20]]; // _Vincenzo Librandi_, Sep 15 2016
%Y Cf. A003266 (for Fibonacci), A003046 (for Catalan), A101690, A135407, A218490.
%K nonn,easy
%O 0,3
%A _Wolfdieter Lang_, May 10 2002
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