A017429 a(n) = (11*n+3)^5.

243, 537824, 9765625, 60466176, 229345007, 656356768, 1564031349, 3276800000, 6240321451, 11040808032, 18424351793, 29316250624, 44840334375, 66338290976, 95388992557, 133827821568, 183765996899

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (6, -15, 20, -15, 6, -1).

Crossrefs

Cf. A000584, A017425.

Programs

Magma

[(11*n+3)^5: n in [0..20]]; // Vincenzo Librandi, Apr 16 2017

Maple

A017429:=n->(11*n+3)^5: seq(A017429(n), n=0..50); # Wesley Ivan Hurt, Apr 14 2017

Mathematica

(* From Harvey P. Dale, Apr 30 2013: (Start) *)
(11*Range[0,20]+3)^5
LinearRecurrence[{6,-15,20,-15,6,-1},{243,537824,9765625,60466176,229345007,656356768},20] (* End *)
CoefficientList[Series[(243 + 536366*x + 6542326*x^2 + 9934926*x^3 + 2279491*x^4 + 32768*x^5)/(x - 1)^6, {x, 0, 50}], x] (* Indranil Ghosh, Apr 15 2017 *)
Table[(11 n + 3)^5, {n, 0, 30}] (* Vincenzo Librandi, Apr 16 2017 *)

PARI

a(n) = (11*n + 3)^5; \\ Indranil Ghosh, Apr 15 2017

Formula

a(0)=243, a(1)=537824, a(2)=9765625, a(3)=60466176, a(4)=229345007, a(5)=656356768, a(n) = 6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Apr 30 2013

G.f.: (243 + 536366*x + 6542326*x^2 + 9934926*x^3 + 2279491*x^4 + 32768*x^5)/(x - 1)^6. - Indranil Ghosh, Apr 15 2017