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 A274985 a(n) = ([n]_phi! - [n]_{1-phi}!)/sqrt(5), where [n]_q! is the q-factorial, phi = (1+sqrt(5))/2. 2
 0, 0, 1, 6, 58, 948, 25992, 1179016, 87713040, 10646068080, 2101395344400, 673242645670320, 349671381118477440, 294206779308703578240, 400822226102433353285760, 883965927408694948620295680, 3155212287401150653204012531200 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Table of n, a(n) for n=0..16. 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 Cf. A274983, A005329, A275706, A276474, A276688, A276987. Sequence in context: A302922 A366298 A337594 * A034982 A156147 A024269 Adjacent sequences: A274982 A274983 A274984 * A274986 A274987 A274988 KEYWORD nonn AUTHOR Vladimir Reshetnikov, Sep 23 2016 STATUS approved

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Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)