A128792 n^3*6^n.

0, 6, 288, 5832, 82944, 972000, 10077696, 96018048, 859963392, 7346640384, 60466176000, 482882881536, 3761479876608, 28694344753152, 215031266279424, 1586874322944000, 11555266180939776, 83160677851987968

Offset

0,2

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (24,-216,864,-1296).

Formula

G.f.: 6*x*(1 + 24*x + 36*x^2)/(1 - 6*x)^4. - Vincenzo Librandi, Feb 08 2013

a(n) = 24*a(n-1) - 216*a(n-2) + 864*a(n-3) - 1296*a(n-4). - Vincenzo Librandi, Feb 09 2013

Mathematica

CoefficientList[Series[6 x *(1+24 x + 36 x^2)/(1-6*x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 08 2013 *)
LinearRecurrence[{24, -216, 864, -1296}, {0, 6, 288, 5832}, 20] (* Harvey P. Dale, Mar 12 2023 *)

Prog

(Magma) [n^3*6^n: n in [0..20]]; // Vincenzo Librandi, Feb 08 2013
(Magma) I:=[0, 6, 288, 5832]; [n le 4 select I[n] else 24*Self(n-1)-216*Self(n-2)+864*Self(n-3)-1296*Self(n-4): n in [1..30]]; // Vincenzo Librandi, Feb 09 2013

Crossrefs

Cf. A036289, A007758.

Sequence in context: A201139 A172660 A203051 * A340540 A027875 A203422

Adjacent sequences: A128789 A128790 A128791 * A128793 A128794 A128795

Keyword

nonn,easy

Author

Mohammad K. Azarian, Apr 07 2007

Status

approved