A128013 a(n) = (n^3 +n)*5^n.

10, 250, 3750, 42500, 406250, 3468750, 27343750, 203125000, 1441406250, 9863281250, 65527343750, 424804687500, 2697753906250, 16833496093750, 103454589843750, 627441406250000, 3761291503906250, 22315979003906250

Offset

1,1

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Index entries for linear recurrences with constant coefficients, signature (20,-150,500,-625).

Formula

G.f.: 10*x(1+5*x+25*x^2)/(1-5*x)^4. - Vincenzo Librandi, Feb 22 2013

a(n) = 20*a(n-1) -150*a(n-2) +500*a(n-3) -625*a(n-4). - Vincenzo Librandi, Feb 23 2013

Mathematica

Table[(n^3 + n) 5^n, {n, 30}] (* or *) CoefficientList[Series[10 (1 + 5 x + 25 x^2)/(1 - 5 x)^4, {x, 0, 30}], x] (* Vincenzo Librandi, Feb 22 2013 *)

Prog

(Magma) [(n^3 + n)*5^n: n in [1..20]]; // Vincenzo Librandi, Feb 22 2013
(Magma) I:=[10, 250, 3750, 42500]; [n le 4 select I[n] else 20*Self(n-1)-150*Self(n-2)+500*Self(n-3)-625*Self(n-4): n in [1..20]]; // Vincenzo Librandi, Feb 23 2013
(PARI) for(n=1, 30, print1((n^3 +n)*5^n, ", ")) \\ G. C. Greubel, May 08 2018

Crossrefs

Cf. A128796, A128960, A128985, A129002.

Sequence in context: A211093 A108792 A265854 * A178021 A134262 A240289

Adjacent sequences: A128010 A128011 A128012 * A128014 A128015 A128016

Keyword

nonn,easy

Author

Mohammad K. Azarian, May 02 2007

Status

approved