A217473 Product of the first n+1 odd-indexed Lucas numbers A000032.

1, 4, 44, 1276, 96976, 19298224, 10054374704, 13714167096256, 48973290700730176, 457851294761126415424, 11206368290573330143917824, 718092873691648422292110244096, 120467978583384630972146706659789056

Offset: 0

Author

Wolfdieter Lang, Oct 12 2012

Keywords

• nonn
• easy

Comments

This sequence is used in A217472 to produce the integer instead of rational Ozeki-Prodinger triangle, and the corresponding sequence A217474.

Crossrefs

Cf. A000032, A001622 (phi), 2*A070825 (product of the first n+1 Lucas numbers).

Cf. A217472, A217474.

Programs

Mathematica

FoldList[Times, LucasL[Range[1, 26, 2]]] (* Amiram Eldar, Jul 09 2025 *)

Formula

a(n) = Product_{i=0..n} L(2*i+1), n >= 0, with the Lucas numbers L=A000032.

a(n) ~ c * phi^(n*(n+2)), where c = Product_{k>=1} (1 - 1/phi^(4*k+2)) = 0.93529381211738925891... . - Amiram Eldar, Jul 09 2025