A128787 n^2*8^n.

0, 8, 256, 4608, 65536, 819200, 9437184, 102760448, 1073741824, 10871635968, 107374182400, 1039382085632, 9895604649984, 92908732547072, 862017116176384, 7916483719987200, 72057594037927936, 650770146155036672

Offset

0,2

Comments

Subsequence of A047351. [Bruno Berselli, Feb 07 2013]

Links

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

Index entries for linear recurrences with constant coefficients, signature (24,-192,512).

Formula

G.f.: 8*x*(1 + 8*x)/(1 - 8*x)^3. - Vincenzo Librandi, Feb 06 2013

a(n) = 24*a(n-1) - 192*a(n-2) + 512*a(n-3). - Vincenzo Librandi, Feb 06 2013

Example

a(1) = 1^2 * 8^1 = 1 * 8 = 8.
a(2) = 2^2 * 8^2 = 4 * 64 = 256.
a(3) = 3^2 * 8^3 = 9 * 512 = 4608.

Mathematica

LinearRecurrence[{24, -192, 512}, {0, 8, 256}, 30] (* or *) CoefficientList[Series[8 x (1 + 8 x)/((1 - 8 x)^3), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)
Table[n^2 8^n, {n, 0, 19}] (* Alonso del Arte, Feb 06 2013 *)

Prog

(Magma) [n^2*8^n: n in [0..20]]; // Vincenzo Librandi, Feb 06 2013

Crossrefs

Cf. A036289, A007758.

Sequence in context: A300176 A291850 A130034 * A013824 A010044 A024290

Adjacent sequences: A128784 A128785 A128786 * A128788 A128789 A128790

Keyword

nonn,easy

Author

Mohammad K. Azarian, Apr 07 2007

Status

approved