A218490 - OEIS

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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

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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