A016785 - OEIS

%I #27 Mar 29 2022 03:00:50

%S 1,262144,40353607,1000000000,10604499373,68719476736,322687697779,

%T 1207269217792,3814697265625,10578455953408,26439622160671,

%U 60716992766464,129961739795077,262144000000000,502592611936843,922190162669056,1628413597910449,2779905883635712

%N a(n) = (3*n + 1)^9.

%H Vincenzo Librandi, <a href="/A016785/b016785.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 From _Amiram Eldar_, Mar 29 2022: (Start)

%F a(n) = A016777(n)^9 = A016779(n)^3.

%F Sum_{n>=0} 1/a(n) = 1618*Pi^9/(55801305*sqrt(3)) + 9841*zeta(9)/3^9. (End)

%p A016785:=n->(3*n+1)^9; seq(A016785(k), k=0..100); # _Wesley Ivan Hurt_, Nov 05 2013

%t Table[(3*n+1)^9, {n,0,100}] (* _Wesley Ivan Hurt_, Nov 05 2013 *)

%t LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,262144,40353607,1000000000,10604499373,68719476736,322687697779,1207269217792,3814697265625,10578455953408},100] (* _Harvey P. Dale_, Aug 17 2014 *)

%o (Magma) [(3*n+1)^9 : n in [0..20]]; // _Vincenzo Librandi_, Sep 28 2011

%Y Cf. A016777, A016778, A016779, A016780, A016781, A016782, A016783, A016784.

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_