A016927 a(n) = (6*n + 1)^7.
1, 823543, 62748517, 893871739, 6103515625, 27512614111, 94931877133, 271818611107, 678223072849, 1522435234375, 3142742836021, 6060711605323, 11047398519097, 19203908986159, 32057708828125, 51676101935731, 80798284478113, 122987386542487, 182803912081669
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
- Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
Programs
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Magma
[(6*n+1)^7: n in [0..40]]; // Vincenzo Librandi, May 04 2011
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Mathematica
(6*Range[0,20]+1)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,823543,62748517,893871739,6103515625,27512614111,94931877133,271818611107},20] (* Harvey P. Dale, May 12 2015 *)
Formula
a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, May 12 2015
From Amiram Eldar, Mar 28 2022: (Start)
a(n) = A016921(n)^7.
Sum_{n>=0} 1/a(n) = 301*Pi^7/(1049760*sqrt(3)) + 138811*zeta(7)/279936. (End)