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A070825 One half of product of first n+1 Lucas numbers A000032. 12
1, 1, 3, 12, 84, 924, 16632, 482328, 22669416, 1722875616, 211913700768, 42170826452832, 13579006117811904, 7074662187380001984, 5963940223961341672512, 8134814465483270041306368 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
LINKS
R. Grünwald, E. Heidel, A. Strätz, M. Sünkel and R. Terbach, Induction on Number Series, Fakultät fur Wirtschaftsinformatik und Angewandte Informatik, Otto-Friedrich-Universität Bamberg, 2012. - N. J. A. Sloane, Feb 07 2013
FORMULA
a(n) = (Product_{k=0..n} L(n))/2 with L(n) := A000032(n).
Sum_{n>=0} 1/a(n) = 1 + A101690. - Amiram Eldar, Nov 09 2020
MATHEMATICA
FoldList[Times, LucasL[Range[0, 20]]]/2 (* or *)
Table[Round[GoldenRatio^(n(n+1)/2) QPochhammer[-1, GoldenRatio-2, n+1]]/2, {n, 0, 20}] (* Vladimir Reshetnikov, Sep 15 2016 *)
PROG
(PARI) a(n) = prod(k=0, n, fibonacci(k+1)+fibonacci(k-1))/2; \\ Michel Marcus, Mar 18 2016
(Magma) [1] cat [&*[Lucas(i+1): i in [0..n]]: n in [0..20]]; // Vincenzo Librandi, Sep 15 2016
CROSSREFS
Cf. A003266 (for Fibonacci), A003046 (for Catalan), A101690, A135407, A218490.
Sequence in context: A032183 A225905 A355322 * A232934 A077047 A074505
KEYWORD
nonn,easy
AUTHOR
Wolfdieter Lang, May 10 2002
STATUS
approved

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Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)