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A135407 Partial products of A000032 (Lucas numbers beginning at 2). 10
2, 2, 6, 24, 168, 1848, 33264, 964656, 45338832, 3445751232, 423827401536, 84341652905664, 27158012235623808, 14149324374760003968, 11927880447922683345024, 16269628930966540082612736 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

This is to A000032 as A003266 is to A000045. a(n) is asymptotic to C*phi^(n*(n+1)/2) where phi=(1+sqrt(5))/2 is the golden ratio and C = 1.3578784076121057013874397... (see A218490). - Corrected and extended by Vaclav Kotesovec, Oct 30 2012

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..95

FORMULA

a(n) = Product_{k=0..n} A000032(k).

C = exp( Sum_{k>=1} 1/(k*(((3-sqrt(5))/2)^k-(-1)^k)) ). - Vaclav Kotesovec, Jun 08 2013

EXAMPLE

a(0) = L(0) = 2.

a(1) = L(0)*L(1) = 2*1 = 2.

a(2) = L(0)*L(1)*L(2) = 2*1*3 = 6.

a(3) = L(0)*L(1)*L(2)*L(3) = 2*1*3*4 = 24.

MATHEMATICA

Rest[FoldList[Times, 1, LucasL[Range[0, 20]]]] (* Harvey P. Dale, Aug 21 2013 *)

Table[Round[GoldenRatio^(n(n+1)/2) QPochhammer[-1, GoldenRatio-2, n+1]], {n, 0, 20}] (* Vladimir Reshetnikov, Sep 14 2016 *)

PROG

(PARI) a(n) = prod(k=0, n, fibonacci(k+1)+fibonacci(k-1)); \\ Michel Marcus, Oct 13 2016

CROSSREFS

Cf. A000032, A000045, A000204, A003266, A070825, A218490.

Sequence in context: A301381 A253093 A052660 * A292831 A076726 A032272

Adjacent sequences:  A135404 A135405 A135406 * A135408 A135409 A135410

KEYWORD

easy,nonn

AUTHOR

Jonathan Vos Post, Dec 09 2007

STATUS

approved

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Last modified January 29 08:12 EST 2020. Contains 331337 sequences. (Running on oeis4.)