A127960 a(n) = n^2*3^n.

0, 3, 36, 243, 1296, 6075, 26244, 107163, 419904, 1594323, 5904900, 21434787, 76527504, 269440587, 937461924, 3228504075, 11019960576, 37321507107, 125524238436, 419576389587, 1394713760400, 4613015762523, 15188432850756

Offset: 0

Author

Mohammad K. Azarian, Apr 07 2007

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (9,-27,27).

Crossrefs

Cf. A036289, A007758, A069996.

Programs

Magma

[n^2*3^n: n in [0..30]]; // Vincenzo Librandi, Feb 07 2013

Mathematica

LinearRecurrence[{9,-27,27}, {0,3,36}, 25] (* or *) CoefficientList[ Series[3*x(1 + 3*x)/(1 - 3*x)^3, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 07 2013 *)

PARI

for(n=0,30, print1(n^2*3^n, ", ")) \\ G. C. Greubel, May 04 2018

Formula

G.f.: 3*x*(1 + 3*x)/(1 - 3*x)^3. - Vincenzo Librandi, Feb 07 2013

a(n) = 9*a(n-1) - 27*a(n-2) + 27*a(n-3). - Vincenzo Librandi, Feb 07 2013

a(n) = 3*A069996(n) for n>0. - Bruno Berselli, Feb 07 2013

E.g.f.: (9*x^2 + 3*x)*exp(3*x). - G. C. Greubel, May 04 2018