A128790 - OEIS

%I #17 Nov 24 2022 14:30:36

%S 0,4,128,1728,16384,128000,884736,5619712,33554432,191102976,

%T 1048576000,5582618624,28991029248,147438174208,736586891264,

%U 3623878656000,17592186044416,84404697300992,400771988324352,1885387563728896

%N n^3*4^n.

%C All terms are congruent to {0, 2, 4} mod 6 (or mod 9 or mod 18). [_Bruno Berselli_, Feb 07 2013]

%H Vincenzo Librandi, <a href="/A128790/b128790.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (16,-96,256,-256)

%F G.f.: 4*x*(1 + 16*x + 16*x^2)/(1 - 4*x)^4. - _Vincenzo Librandi_, Feb 07 2013

%t CoefficientList[Series[4*x*(1 + 16*x + 16*x^2)/(1 - 4*x)^4, {x, 0, 30}], x] (* _Vincenzo Librandi_, Feb 07 2013 *)

%t Table[n^3 4^n,{n,0,20}] (* or *) LinearRecurrence[{16,-96,256,-256},{0,4,128,1728},20] (* _Harvey P. Dale_, Nov 24 2022 *)

%o (Magma) [n^3*4^n: n in [0..30]]; // _Vincenzo Librandi_, Feb 07 2013

%Y Cf. A036289; A007758.

%K nonn,easy

%O 0,2

%A _Mohammad K. Azarian_, Apr 07 2007