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

0,3

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).

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)

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 *)

Prog

(PARI) vector(31, n, my(m=n-1); 3^(m-1)*m^3) \\ G. C. Greubel, Feb 08 2020
(Magma) [3^(n-1)*n^3: n in [0..30]]; // G. C. Greubel, Feb 08 2020
(Sage) [3^(n-1)*n^3 for n in (0..30)] # G. C. Greubel, Feb 08 2020
(GAP) List([0..30], n-> 3^(n-1)*n^3 ); # G. C. Greubel, Feb 08 2020

Crossrefs

Cf. A014477, A086604, A086605.

Sequence in context: A052652 A052732 A267060 * A304835 A281076 A300397

Adjacent sequences: A086600 A086601 A086602 * A086604 A086605 A086606

Keyword

easy,nonn

Author

Paul Barry, Jul 23 2003

Status

approved