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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.

2, 1, 2, -2, 20, -190, 3240, -90800, 4174920, -313173840, 38204662320, -7564715117520, 2428250059593600, -1262694691720176000, 1063187432567808662400, -1449125250052431355430400, 3196769645011428154428883200, -11412468527893653264760022630400

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

OFFSET

0,1

LINKS

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, q-Pochhammer Symbol, Golden Ratio.

FORMULA

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

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

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

MATHEMATICA

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 *)

CROSSREFS

Cf. A274983, A276474, A276987, A276991.

Sequence in context: A229232 A092186 A138262 * A127510 A328362 A158810

Adjacent sequences: A276987 A276988 A276989 * A276991 A276992 A276993

KEYWORD

sign

AUTHOR

Vladimir Reshetnikov, Sep 24 2016

STATUS

approved

URL: https://oeis.org/A276990

⇱ A276990 - OEIS