A017333 a(n) = (10*n + 5)^5.

3125, 759375, 9765625, 52521875, 184528125, 503284375, 1160290625, 2373046875, 4437053125, 7737809375, 12762815625, 20113571875, 30517578125, 44840334375, 64097340625, 89466096875, 122298103125, 164130859375, 216699865625, 281950621875, 362050628125, 459401384375

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, A016757, A017329.

Cf. A272914 (first comment). [Bruno Berselli, May 26 2016]

Programs

Magma

[(10*n+5)^5: n in [0..25]]; // Vincenzo Librandi, Aug 02 2011

Mathematica

(10*Range[0,20]+5)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{3125,759375,9765625,52521875,184528125,503284375},20] (* Harvey P. Dale, May 15 2018 *)

Formula

G.f.: 3125*(x+1)*(x^4+236*x^3+1446*x^2+236*x+1)/(x-1)^6. - Colin Barker, Nov 14 2012

From Amiram Eldar, Apr 18 2023: (Start)

a(n) = A017329(n)^5.

a(n) = 5^5 * A016757(n).

Sum_{n>=0} 1/a(n) = 31*zeta(5)/100000.

Sum_{n>=0} (-1)^n/a(n) = Pi^5/960000. (End)