A016937 a(n) = (6*n + 2)^5.
32, 32768, 537824, 3200000, 11881376, 33554432, 79235168, 164916224, 312500000, 550731776, 916132832, 1453933568, 2219006624, 3276800000, 4704270176, 6590815232, 9039207968, 12166529024, 16105100000, 21003416576, 27027081632, 34359738368, 43204003424, 53782400000
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
- Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
Programs
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Magma
[(6*n+2)^5: n in [0..30]]; // Vincenzo Librandi, May 04 2011
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Mathematica
(6*Range[0,20]+2)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{32,32768,537824,3200000,11881376,33554432},20] (* Harvey P. Dale, Dec 13 2012 *)
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, Dec 13 2012
From Amiram Eldar, Mar 29 2022: (Start)
a(n) = A016933(n)^5.
a(n) = 32*A016781(n).
Sum_{n>=0} 1/a(n) = Pi^5/(11664*sqrt(3)) + 121*zeta(5)/7776. (End)