A135407 Partial products of A000032 (Lucas numbers beginning at 2).

2, 2, 6, 24, 168, 1848, 33264, 964656, 45338832, 3445751232, 423827401536, 84341652905664, 27158012235623808, 14149324374760003968, 11927880447922683345024, 16269628930966540082612736

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: A253093 A052660 A374399 * A374400 A292831 A076726

Adjacent sequences: A135404 A135405 A135406 * A135408 A135409 A135410

Keyword

easy,nonn

Author

Jonathan Vos Post, Dec 09 2007

Status

approved