A017201 a(n) = (9*n + 3)^5.

243, 248832, 4084101, 24300000, 90224199, 254803968, 601692057, 1252332576, 2373046875, 4182119424, 6956883693, 11040808032, 16850581551, 24883200000, 35723051649, 50049003168, 68641485507, 92389579776, 122298103125, 159494694624, 205236901143, 260919263232

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Crossrefs

Cf. A013663, A016781, A017197.

Programs

Magma

[(9*n+3)^5: n in [0..30]]; // Vincenzo Librandi, Jul 23 2011

Mathematica

(9*Range[0,20]+3)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{243,248832,4084101,24300000,90224199,254803968},20] (* Harvey P. Dale, Jul 27 2019 *)

Formula

G.f.: 243*(1 + 1018*x + 10678*x^2 + 14498*x^3 + 2933*x^4 + 32*x^5)/(x-1)^6. - R. J. Mathar, Jul 14 2016

From Amiram Eldar, Oct 03 2024: (Start)

a(n) = A017197(n)^5 = 3^5 * A016781(n).

Sum_{n>=0} 1/a(n) = 2*Pi^5/(177147*sqrt(3)) + 121*zeta(5)/59049. (End)