A128789 n^3*2^n.

0, 2, 32, 216, 1024, 4000, 13824, 43904, 131072, 373248, 1024000, 2725888, 7077888, 17997824, 44957696, 110592000, 268435456, 643956736, 1528823808, 3596091392, 8388608000, 19421724672, 44660948992, 102064193536, 231928233984

Offset

0,2

Links

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

Index entries for linear recurrences with constant coefficients, signature (8,-24,32,-16).

Formula

G.f.: 2*x*(1 + 8*x + 4*x^2)/(1 - 2*x)^4. - Vincenzo Librandi, Feb 07 2013

a(0)=0, a(1)=2, a(2)=32, a(3)=216, a(n)=8*a(n-1)-24*a(n-2)+ 32*a(n-3)- 16*a(n-4). - Harvey P. Dale, Jun 14 2013

E.g.f.: exp(2*x)*(2*x + 12*x^2 + 8*x^3). - Geoffrey Critzer, Aug 28 2013

Sum_{n>=1} 1/a(n) = (log(2))^3/6 - Pi^2*log(2)/12 + 7*Zeta(3)/8 = 0.53721319360804020094... . - Vaclav Kotesovec, Feb 15 2015

Mathematica

CoefficientList[Series[2 x (1 + 8 x + 4 x^2)/(1 - 2 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 07 2013 *)
Table[n^3 2^n, {n, 0, 30}] (* or *) LinearRecurrence[{8, -24, 32, -16}, {0, 2, 32, 216}, 30] (* Harvey P. Dale, Jun 14 2013 *)

Prog

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

Crossrefs

Cf. A036289, A007758.

Sequence in context: A244730 A169833 A228582 * A356345 A053316 A053053

Adjacent sequences: A128786 A128787 A128788 * A128790 A128791 A128792

Keyword

nonn,easy

Author

Mohammad K. Azarian, Apr 07 2007

Status

approved