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a(n) = (6*n + 2)^9.
4

%I #22 Mar 29 2022 02:54:41

%S 512,134217728,20661046784,512000000000,5429503678976,35184372088832,

%T 165216101262848,618121839509504,1953125000000000,5416169448144896,

%U 13537086546263552,31087100296429568,66540410775079424,134217728000000000,257327417311663616,472161363286556672

%N a(n) = (6*n + 2)^9.

%H Vincenzo Librandi, <a href="/A016941/b016941.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

%F 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_, Sep 21 2013

%F From _Amiram Eldar_, Mar 29 2022: (Start)

%F a(n) = A016933(n)^9 = A016935(n)^3.

%F a(n) = 2^9*A016785(n).

%F Sum_{n>=0} 1/a(n) = 809*Pi^9/(14285134080*sqrt(3)) + 9841*zeta(9)/10077696. (End)

%t (6*Range[0,20]+2)^9 (* or *) LinearRecurrence[ {10,-45,120,-210,252,-210,120,-45,10,-1},{512,134217728,20661046784,512000000000,5429503678976,35184372088832,165216101262848,618121839509504,1953125000000000,5416169448144896},20] (* _Harvey P. Dale_, Sep 21 2013 *)

%o (Magma) [(6*n+2)^9: n in [0..25]]; // _Vincenzo Librandi_, May 05 2011

%Y Cf. A016785, A016933, A016934, A016935, A016936, A016937, A016938, A016939, A016940.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_