A168075 Expansion of (1+27x^2-54x^3)/((1+3x)^2*(1-3x+9 x^2)).

1, -3, 36, -189, 567, -2430, 9477, -28431, 104976, -373977, 1121931, -3897234, 13286025, -39858075, 133923132, -444816117, 1334448351, -4390765542, 14334558093, -43003674279, 139471376040, -449795187729, 1349385563187, -4330586226042, 13839047287569

Offset: 0

Author

Paul Barry, Nov 18 2009

Keywords

• easy
• sign

Comments

Hankel transform of A168076.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (-3,0,-27,-81).

Crossrefs

Cf. A061891, A168076.

Programs

Magma

I:=[1,-3,36,-189]; [n le 4 select I[n] else -3*Self(n-1)-27*Self(n-3)-81*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Jul 10 2016

Mathematica

LinearRecurrence[{-3, 0, -27, -81}, {1, -3, 36, -189}, 50] (* G. C. Greubel, Jul 09 2016 *)
CoefficientList[Series[(1 + 27 x^2 - 54 x^3) / ((1 + 3 x)^2 (1 - 3 x + 9 x^2)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 10 2016 *)

PARI

Vec((1+27*x^2-54*x^3)/((1+3*x)^2*(1-3*x+9*x^2))+ O(x^30)) \\ Michel Marcus, Dec 03 2014

Formula

a(n) = (-3)^n*A061891(n).

a(n) = 2*(-3)^n*n + 3^n*(sin(Pi*n/3)/sqrt(3) + cos(Pi*n/3)). - Ilya Gutkovskiy, Jul 10 2016

Extensions

Corrected by R. J. Mathar, Dec 03 2014