A016757 a(n) = (2*n+1)^5.

1, 243, 3125, 16807, 59049, 161051, 371293, 759375, 1419857, 2476099, 4084101, 6436343, 9765625, 14348907, 20511149, 28629151, 39135393, 52521875, 69343957, 90224199, 115856201, 147008443, 184528125, 229345007, 282475249, 345025251, 418195493, 503284375, 601692057

Offset

0,2

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).

Formula

G.f.: (1+x)*(x^4 +236*x^3 +1446*x^2 +236*x +1)/(x-1)^6 . - R. J. Mathar, Jul 07 2017

From Amiram Eldar, Oct 10 2020: (Start)

Sum_{n>=0} 1/a(n) = 31*zeta(5)/32.

Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/1536 (A175571). (End)

Mathematica

Table[(2*n+1)^5, {n, 0, 30}] (* G. C. Greubel, Sep 15 2018 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {1, 243, 3125, 16807, 59049, 161051}, 30] (* Harvey P. Dale, Sep 04 2022 *)

Prog

(Magma) [(2*n+1)^5: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011
(Maxima) makelist((2*n+1)^5, n, 0, 20); /* Martin Ettl, Nov 12 2012 */
(PARI) vector(30, n, n--; (2*n+1)^5) \\ G. C. Greubel, Sep 15 2018

Crossrefs

Cf. A175571.

Sequence in context: A269056 A209507 A226777 * A133550 A029700 A224003

Adjacent sequences: A016754 A016755 A016756 * A016758 A016759 A016760

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved