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A276990 a(n) = (phi; phi)_n + (1-phi; 1-phi)_n, where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio. 1

%I #8 Sep 25 2016 05:52:54

%S 2,1,2,-2,20,-190,3240,-90800,4174920,-313173840,38204662320,

%T -7564715117520,2428250059593600,-1262694691720176000,

%U 1063187432567808662400,-1449125250052431355430400,3196769645011428154428883200,-11412468527893653264760022630400

%N a(n) = (phi; phi)_n + (1-phi; 1-phi)_n, where (q; q)_n is the q-Pochhammer symbol, phi = (1+sqrt(5))/2 is the golden ratio.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/q-PochhammerSymbol.html">q-Pochhammer Symbol</a>, <a href="http://mathworld.wolfram.com/GoldenRatio.html">Golden Ratio</a>.

%F (phi; phi)_n = (a(n) + A276991(n)*sqrt(5))/2.

%F (1-phi; 1-phi)_n = (a(n) - A276991(n)*sqrt(5))/2.

%F a(n) ~ c * (-1)^n * phi^(n*(n+1)/2), where c = (1/phi)_inf = A276987 = 0.1208019218617061294237231569887920563043992516794...

%t Round@Table[QPochhammer[GoldenRatio, GoldenRatio, n] + QPochhammer[1 - GoldenRatio, 1 - GoldenRatio, n], {n, 0, 20}] (* Round is equivalent to FullSimplify here, but is much faster *)

%Y Cf. A274983, A276474, A276987, A276991.

%K sign

%O 0,1

%A _Vladimir Reshetnikov_, Sep 24 2016

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Last modified July 21 16:10 EDT 2024. Contains 374475 sequences. (Running on oeis4.)