A017099 a(n) = (8*n + 2)^11.
2048, 100000000000, 64268410079232, 3670344486987776, 70188843638032384, 717368321110468608, 4882812500000000000, 24986644000165537792, 103510234140112521216, 364375289404334925824, 1127073856954876807168, 3138105960900000000000, 8007313507497959524352
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
Programs
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Magma
[(8*n+2)^11: n in [0..20]]; // Vincenzo Librandi, Jul 12 2011
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Mathematica
(8*Range[0,20]+2)^11 (* Harvey P. Dale, Dec 12 2012 *)
Formula
From Amiram Eldar, Apr 24 2023: (Start)
a(n) = A017089(n)^11.
a(n) = 2^11*A016823(n).
Sum_{n>=0} 1/a(n) = 50521*Pi^11/60881161420800 + 2047*zeta(11)/8388608. (End)
a(n) = 12*a(n-1) - 66*a(n-2) + 220*a(n-3) - 495*a(n-4) + 792*a(n-5) - 924*a(n-6) + 792*a(n-7) - 495*a(n-8) + 220*a(n-9) - 66*a(n-10) + 12*a(n-11) - a(n-12). - Wesley Ivan Hurt, Jan 20 2024