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

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. A175571.

Programs

Magma

[(2*n+1)^5: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011

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 *)

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

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)