A086603 a(n) = n^3*3^(n-1).

0, 1, 24, 243, 1728, 10125, 52488, 250047, 1119744, 4782969, 19683000, 78594219, 306110016, 1167575877, 4374822312, 16142520375, 58773123072, 211488540273, 753145430616, 2657317134051, 9298091736000, 32291110337661

Offset: 0

Author

Paul Barry, Jul 23 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A086604. Second binomial transform of A086605.

Links

• G. C. Greubel, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (12,-54,108,-81).

Crossrefs

Cf. A014477, A086604, A086605.

Programs

GAP

List([0..30], n-> 3^(n-1)*n^3 ); # G. C. Greubel, Feb 08 2020

Magma

[3^(n-1)*n^3: n in [0..30]]; // G. C. Greubel, Feb 08 2020

Maple

seq( 3^(n-1)*n^3, n=0..30); # G. C. Greubel, Feb 08 2020

Mathematica

Table[n^3 3^(n-1),{n,0,30}]  (* Harvey P. Dale, Mar 12 2011 *)

PARI

vector(31, n, my(m=n-1); 3^(m-1)*m^3) \\ G. C. Greubel, Feb 08 2020

Sage

[3^(n-1)*n^3 for n in (0..30)] # G. C. Greubel, Feb 08 2020

Formula

From G. C. Greubel, Feb 08 2020: (Start)

G.f.: x*(1 + 12*x + 9*x^2)/(1-3*x)^4.

E.g.f.: x*(1 + 9*x + 9*x^2)*exp(x). (End)