OFFSET
0,1
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
From Ilya Gutkovskiy, Jun 16 2016: (Start)
G.f.: (32 + 2933*x + 14498*x^2 + 10678*x^3 + 1018*x^4 + x^5)/(1 - x)^6.
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). (End)
From Amiram Eldar, Mar 31 2022: (Start)
a(n) = A016789(n)^5.
Sum_{n>=0} 1/a(n) = 121*zeta(5)/243 - 2*Pi^5/(729*sqrt(3)). (End)
MATHEMATICA
Table[(3n+2)^5, {n, 0, 100}] (* Mohammad K. Azarian, Jun 15 2016 *)
LinearRecurrence[{6, -15, 20, -15, 6, -1}, {32, 3125, 32768, 161051, 537824, 1419857}, 30] (* Harvey P. Dale, May 10 2024 *)
PROG
(Magma) [(3*n+2)^5 : n in [0..30]]; // Vincenzo Librandi, Sep 29 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved