A218490 Decimal expansion of Lucas factorial constant.

1, 3, 5, 7, 8, 7, 8, 4, 0, 7, 6, 1, 2, 1, 0, 5, 7, 0, 1, 3, 8, 7, 4, 3, 9, 7, 0, 9, 7, 6, 0, 6, 0, 7, 1, 8, 5, 5, 7, 8, 6, 0, 5, 8, 6, 5, 2, 9, 5, 6, 7, 8, 7, 0, 4, 4, 9, 6, 8, 7, 8, 2, 5, 4, 3, 8, 4, 0, 7, 1, 9, 1, 1, 0, 3, 4, 8, 6, 2, 3, 3, 6, 8, 7, 7, 1, 4

Offset: 1

Author

Vaclav Kotesovec, Oct 30 2012

Keywords

• nonn
• cons

Comments

The Lucas factorial constant is associated with the Lucas factorial A135407.

Examples

			1.35787840761210570138743970976060718557860586529567870449687825438407191103...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A062073, A135407, A070825, A003266, A000032, A000045, A186269, A001622.

Programs

Mathematica

RealDigits[QPochhammer[-1, -1/GoldenRatio^2], 10, 105][[1]] (* slightly modified by Robert G. Wilson v, Dec 21 2017 *)

PARI

prodinf(j=0, 1 + ((sqrt(5) - 3)/2)^j) \\ Iain Fox, Dec 21 2017

Formula

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

Equals Product_{k=0..infinity} (1 + (-1)^k/phi^(2*k)). - G. C. Greubel, Dec 23 2017

Equals lim_{n->oo} A135407(n)/phi^(n*(n+1)/2), where phi is the golden ratio (A001622). - Amiram Eldar, Jan 23 2022