A016793 a(n) = (3*n + 2)^5.
32, 3125, 32768, 161051, 537824, 1419857, 3200000, 6436343, 11881376, 20511149, 33554432, 52521875, 79235168, 115856201, 164916224, 229345007, 312500000, 418195493, 550731776, 714924299, 916132832, 1160290625, 1453933568, 1804229351, 2219006624, 2706784157, 3276800000
Offset: 0
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).
Programs
-
Magma
[(3*n+2)^5 : n in [0..30]]; // Vincenzo Librandi, Sep 29 2011
-
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 *)
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)