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A218490 Decimal expansion of Lucas factorial constant. 7
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 (list; constant; graph; refs; listen; history; text; internal format)
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

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Last modified February 6 20:45 EST 2023. Contains 360111 sequences. (Running on oeis4.)