login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Vincenzo Librandi, Table of n, a(n) for n = 0..90

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: A147835 A032183 A225905 * A232934 A077047 A074505

Adjacent sequences:  A070822 A070823 A070824 * A070826 A070827 A070828

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, May 10 2002

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified April 15 20:35 EDT 2021. Contains 342977 sequences. (Running on oeis4.)