OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, q-Factorial, Golden Ratio.
FORMULA
a(n) ~ c * phi^(n*(n+3)/2), where c = QPochhammer(phi-1) = A276987 = 0.1208019218617061294237231569887920563043992516794... . - Vaclav Kotesovec, Sep 24 2016
From Vladimir Reshetnikov, Sep 24 2016 (Start)
[n]_phi! = (a(n) + A274985(n)*sqrt(5))/2.
[n]_{1-phi}! = (a(n) - A274985(n)*sqrt(5))/2. (End)
EXAMPLE
For n = 3, [3]_phi! = 1060 + 474*sqrt(5), so a(5) = 2*1060 = 2120 and A274985(5) = 2*474 = 948.
MATHEMATICA
Round@Table[QFactorial[n, GoldenRatio] + QFactorial[n, 1 - GoldenRatio], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Reshetnikov, Sep 23 2016
STATUS
approved