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%I #31 Sep 08 2022 08:44:41
%S 0,512,262144,10077696,134217728,1000000000,5159780352,20661046784,
%T 68719476736,198359290368,512000000000,1207269217792,2641807540224,
%U 5429503678976,10578455953408,19683000000000,35184372088832,60716992766464,101559956668416,165216101262848
%N a(n) = (2*n)^9.
%H Vincenzo Librandi, <a href="/A016749/b016749.txt">Table of n, a(n) for n = 0..10000</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_, Jan 13 2013
%F From _Amiram Eldar_, Oct 11 2020: (Start)
%F Sum_{n>=1} 1/a(n) = zeta(9)/512.
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 255*zeta(9)/131072. (End)
%p A016749:=n->(2*n)^9: seq(A016749(n), n=0..30); # _Wesley Ivan Hurt_, Sep 15 2018
%t Table[(2n)^9, {n, 0, 40}] (* _Stefan Steinerberger_, Apr 08 2006 *)
%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45, 10, -1}, {0,512, 262144, 10077696, 134217728, 1000000000, 5159780352, 20661046784, 68719476736, 198359290368}, 20] (* _Harvey P. Dale_, Jan 13 2013 *)
%o (Magma) [(2*n)^9: n in [0..20]]; // _Vincenzo Librandi_, Sep 05 2011
%o (PARI) vector(30, n, n--; (2*n)^9) \\ _G. C. Greubel_, Sep 15 2018
%Y Cf. A016761.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
%E More terms from _Stefan Steinerberger_, Apr 08 2006
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