OFFSET
0,4
LINKS
Eric Weisstein's World of Mathematics, q-Factorial, Golden Ratio.
FORMULA
[n]_phi! = (A274983(n) + a(n)*sqrt(5))/2.
[n]_{1-phi}! = (A274983(n) - a(n)*sqrt(5))/2.
a(n) ~ c * phi^(n*(n+3)/2) / sqrt(5), where c = QPochhammer(phi-1) = A276987 = 0.1208019218617061294237231569887920563043992516794... . - Vaclav Kotesovec, Sep 24 2016
EXAMPLE
For n = 3, [3]_phi! = 1060 + 474*sqrt(5), so A274983(5) = 2*1060 = 2120 and a(5) = 2*474 = 948.
MATHEMATICA
Round@Table[(QFactorial[n, GoldenRatio] - QFactorial[n, 1 - GoldenRatio])/Sqrt[5], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Reshetnikov, Sep 23 2016
STATUS
approved