A247525 a(n) = 5 * a(n-1) - 2 * a(n-1)^2 / a(n-2), with a(0) = 1, a(1) = 2.

1, 2, 2, 6, -6, -42, 378, 8694, -356454, -31011498, 5240943162, 1797643504566, -1224195226609446, -1673474874775112682, 4566912933261282509178, 24949045354406386347639414, -272468524315472145302570040294, -5952619850720119958425247670303018

Offset: 0

Author

Michael Somos, Sep 18 2014

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..83

Crossrefs

Cf. A140966.

Programs

Magma

I:=[1, 2]; [n le 2 select I[n] else 5*Self(n-1) - 2*Self(n-1)^2/Self(n-2): n in [1..30]]; // G. C. Greubel, Aug 05 2018

Mathematica

RecurrenceTable[{a[n] == 5*a[n - 1] - 2*a[n - 1]^2/a[n - 2], a[0] == 1, a[1] == 2}, a, {n, 0, 50}] (* G. C. Greubel, Aug 05 2018 *)

PARI

{a(n) = if( n<0, 1 / prod(k=1, -n, (5 + (-2)^-k) / 3), prod(k=0, n-1, (5 + (-2)^k) / 3))};

Formula

0 = a(n)*(-5*a(n+1) + a(n+2)) + a(n+1)*(+2*a(n+1)) for all n in Z.

a(n+1) = a(n) * A140966(n) for all n in Z.