A016973 a(n) = (6*n + 5)^5.

3125, 161051, 1419857, 6436343, 20511149, 52521875, 115856201, 229345007, 418195493, 714924299, 1160290625, 1804229351, 2706784157, 3939040643, 5584059449, 7737809375, 10510100501, 14025517307, 18424351793, 23863536599, 30517578125, 38579489651, 48261724457

Offset

0,1

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).

Formula

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, Sep 24 2014

G.f.: (3125 + 142301*x + 500426*x^2 + 270466*x^3 + 16801*x^4 + x^5)/(-1+x)^6. - Harvey P. Dale, Aug 13 2021

From Amiram Eldar, Apr 01 2022: (Start)

a(n) = A016969(n)^5.

Sum_{n>=0} 1/a(n) = 3751*zeta(5)/7776 - 11*Pi^5/(3888*sqrt(3)). (End)

Mathematica

(6*Range[0, 20]+5)^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {3125, 161051, 1419857, 6436343, 20511149, 52521875}, 20] (* Harvey P. Dale, Sep 24 2014 *)

Prog

(Magma) [(6*n+5)^5: n in [0..30]]; // Vincenzo Librandi, May 07 2011

Crossrefs

Cf. A016969, A016970, A016971, A016972.

Subsequence of A000584.

Sequence in context: A016817 A115791 A016853 * A017045 A017129 A017225

Adjacent sequences: A016970 A016971 A016972 * A016974 A016975 A016976

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved