A128784 a(n) = n^2*5^n.

0, 5, 100, 1125, 10000, 78125, 562500, 3828125, 25000000, 158203125, 976562500, 5908203125, 35156250000, 206298828125, 1196289062500, 6866455078125, 39062500000000, 220489501953125, 1235961914062500, 6885528564453125, 38146972656250000, 210285186767578125

Offset

0,2

Links

Harvey P. Dale, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (15,-75,125).

Formula

From Harvey P. Dale, Dec 30 2011: (Start)

a(n) = 15*a(n-1) - 75*a(n-2) + 125*a(n-3), a(0)=0, a(1)=5, a(2)=100.

G.f.: -5*x*(5*x+1)/(5*x-1)^3. (End)

E.g.f.: 5*x*(5*x+1)*exp(5*x). - Elmo R. Oliveira, Dec 24 2025

Mathematica

Table[n^2 5^n, {n, 0, 20}] (* Harvey P. Dale, Dec 30 2011 *)
(* Alternative: *)
LinearRecurrence[{15, -75, 125}, {0, 5, 100}, 20] (* Harvey P. Dale, Dec 30 2011 *)

Prog

(PARI) a(n)=n^2*5^n \\ Charles R Greathouse IV, May 16 2018

Crossrefs

Cf. A007758, A036289.

Sequence in context: A156276 A322715 A208348 * A369535 A078534 A380242

Adjacent sequences: A128781 A128782 A128783 * A128785 A128786 A128787

Keyword

nonn,easy,changed

Author

Mohammad K. Azarian, Apr 07 2007

Status

approved