A017097 a(n) = (8*n + 2)^9.
512, 1000000000, 198359290368, 5429503678976, 60716992766464, 406671383849472, 1953125000000000, 7427658739644928, 23762680013799936, 66540410775079424, 167619550409708032, 387420489000000000, 833747762130149888, 1689478959002692096, 3251948521156637184, 5987402799531080192
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
Programs
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Magma
[(8*n+2)^9: n in [0..20]]; // Vincenzo Librandi, Jul 12 2011
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Mathematica
(8*Range[0,30]+2)^9 (* Harvey P. Dale, Dec 15 2011 *)
Formula
a(0)=512, a(1)=1000000000, a(2)=198359290368, a(3)=5429503678976, a(4)=60716992766464, a(5)=406671383849472, a(6)=1953125000000000, a(7)=7427658739644928, a(8)=23762680013799936, a(9)=66540410775079424, a(n)=10*a(n-1)-45*a(n-2)+120*a(n-3)-210*a(n-4)+252*a(n-5)- 210*a(n-6)+ 120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - Harvey P. Dale, Dec 15 2011
From Amiram Eldar, Apr 24 2023: (Start)
a(n) = A017089(n)^9.
a(n) = 2^9*A016821(n).
Sum_{n>=0} 1/a(n) = 277*Pi^9/8455716864 + 511*zeta(9)/524288. (End)