A017338 a(n) = (10*n + 5)^10.
9765625, 576650390625, 95367431640625, 2758547353515625, 34050628916015625, 253295162119140625, 1346274334462890625, 5631351470947265625, 19687440434072265625, 59873693923837890625, 162889462677744140625, 404555773570791015625, 931322574615478515625
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Programs
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Magma
[(10*n+5)^10: n in [0..10]]; // Vincenzo Librandi, Aug 02 2011
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Mathematica
(10 Range[0,20]+5)^10 (* or *) LinearRecurrence[{11,-55,165,-330,462,-462,330,-165,55,-11,1},{9765625,576650390625,95367431640625,2758547353515625,34050628916015625,253295162119140625,1346274334462890625,5631351470947265625,19687440434072265625,59873693923837890625,162889462677744140625},20] (* Harvey P. Dale, Jul 18 2021 *)
Formula
G.f.: -9765625*(x^10 + 59038*x^9 + 9116141*x^8 + 178300904*x^7 + 906923282*x^6 + 1527092468*x^5 + 906923282*x^4 + 178300904*x^3 + 9116141*x^2 + 59038*x + 1)/(x-1)^11. - Colin Barker, Nov 14 2012
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^10.
a(n) = 5^10 * A016762(n).
Sum_{n>=0} 1/a(n) = 31*Pi^10/28350000000000. (End)