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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved