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A247540 a(n) = 2*a(n-1) - 3*a(n-1)^2 / a(n-2), with a(0) = a(1) = 1. 1
1, 1, -1, -5, 65, 2665, -322465, -117699725, 128645799425, 422086867913425, -4153756867136015425, -122639671502190855423125, 10862563623963550637392450625, 2886411268723218638918559372525625, -2300934493386669693418957707961899750625 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..60

FORMULA

0 = a(n)*(-2*a(n+1) + a(n+2)) + a(n+1)*(+3*a(n+1)) for all n in Z.

a(n+1) = a(n) * (-1)^n * A046717(n) for all n in Z.

a(1-n) = (-3)^(n*(n-1)/2) / a(n) for all n in Z.

MATHEMATICA

RecurrenceTable[{a[n] == 2*a[n-1] - 3*a[n-1]^2/a[n-2], a[0]==1, a[1]==1}, a, {n, 0, 30}] (* G. C. Greubel, Aug 04 2018 *)

PROG

(PARI) {a(n) = if( n<0, 1 / prod(k=1, -n, (1 + (-3)^-k) / 2), prod(k=0, n-1, (1 + (-3)^k) / 2))};

(Haskell)

a247540 n = a247540_list !! n

a247540_list = 1 : 1 : zipWith (-)

   (map (* 2) xs) (zipWith div (map ((* 3) . (^ 2)) xs) a247540_list)

   where xs = tail a247540_list

-- Reinhard Zumkeller, Sep 20 2014

(MAGMA) I:=[1, 1]; [n le 2 select I[n] else 2*Self(n-1) - 3*Self(n-1)^2/Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 04 2018

CROSSREFS

Cf. A046717.

Sequence in context: A195196 A012635 A196975 * A171800 A195244 A162080

Adjacent sequences:  A247537 A247538 A247539 * A247541 A247542 A247543

KEYWORD

sign

AUTHOR

Michael Somos, Sep 18 2014

STATUS

approved

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Last modified October 20 19:37 EDT 2021. Contains 348118 sequences. (Running on oeis4.)