A152692 a(n) = n*3^n - n*2^n - n*1^n.

0, 0, 8, 54, 256, 1050, 3984, 14406, 50432, 172530, 580240, 1926078, 6328128, 20619690, 66732176, 214742070, 687698944, 2193154530, 6968850192, 22073006382, 69714716480, 219623377050, 690291036688, 2165100175014

Offset: 0

Author

Vladimir Joseph Stephan Orlovsky, Dec 10 2008

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A152691.

Programs

Magma

[n*3^n-n*2^n-n*1^n: n in [0..30]]; // Vincenzo Librandi, Sep 05 2011

Mathematica

Table[n(3^n-2^n-1),{n,0,30}] (* Harvey P. Dale, Oct 20 2013 *)
CoefficientList[Series[-(2 x^2 (-4 + 21 x - 36 x^2 + 21 x^3))/(-1 + 6 x - 11 x^2 + 6 x^3)^2, {x, 0, 50}], x] (* Stefano Spezia, Sep 04 2018 *)

PARI

vector(30, n, n--; n*(3^n-2^n-1)) \\ G. C. Greubel, Sep 02 2018

Formula

From R. J. Mathar, Dec 12 2008: (Start)

a(n) = (-1)^(n+1)*n*A083321(n).

G.f.: 2*x^2*(4-21*x+36*x^2-21*x^3)/((1-x)^2*(1-3*x)^2*(1-2*x)^2). (End)

E.g.f.: x*(3*exp(3*x) - 2*exp(2*x) - exp(x)). - G. C. Greubel, Sep 02 2018

Extensions

Offset changed from 1 to 0 by Vincenzo Librandi, Sep 05 2011