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

1,2

Comments

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

Links

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

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

Example

1.35787840761210570138743970976060718557860586529567870449687825438407191103...

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A131979 A335894 A101496 * A161696 A196084 A008508

Adjacent sequences: A218487 A218488 A218489 * A218491 A218492 A218493

Keyword

nonn,cons

Author

Vaclav Kotesovec, Oct 30 2012

Status

approved