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A274983

a(n) = [n]_phi! + [n]_{1-phi}!, where [n]_q! is the q-factorial, phi = (1+sqrt(5))/2.

2, 2, 3, 14, 130, 2120, 58120, 2636360, 196132320, 23805331920, 4698862837680, 1505416321070640, 781888977967152000, 657866357975539785600, 896265744457831561756800, 1976607903479486428467148800, 7055269158071576119808840371200

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..16.

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

Cf. A274985, A005329, A275706, A276474, A276688, A276987.

Sequence in context: A275565 A275090 A373310 * A153938 A060790 A109843

Adjacent sequences: A274980 A274981 A274982 * A274984 A274985 A274986

KEYWORD

nonn

AUTHOR

Vladimir Reshetnikov, Sep 23 2016

STATUS

approved

URL: https://oeis.org/A274983

⇱ A274983 - OEIS