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