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a(n) = (9*n + 3)^5.
1

%I #19 Oct 03 2024 03:47:26

%S 243,248832,4084101,24300000,90224199,254803968,601692057,1252332576,

%T 2373046875,4182119424,6956883693,11040808032,16850581551,24883200000,

%U 35723051649,50049003168,68641485507,92389579776,122298103125,159494694624,205236901143,260919263232

%N a(n) = (9*n + 3)^5.

%H Vincenzo Librandi, <a href="/A017201/b017201.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F G.f.: 243*(1 + 1018*x + 10678*x^2 + 14498*x^3 + 2933*x^4 + 32*x^5)/(x-1)^6. - _R. J. Mathar_, Jul 14 2016

%F From _Amiram Eldar_, Oct 03 2024: (Start)

%F a(n) = A017197(n)^5 = 3^5 * A016781(n).

%F Sum_{n>=0} 1/a(n) = 2*Pi^5/(177147*sqrt(3)) + 121*zeta(5)/59049. (End)

%t (9*Range[0,20]+3)^5 (* or *) LinearRecurrence[{6,-15,20,-15,6,-1},{243,248832,4084101,24300000,90224199,254803968},20] (* _Harvey P. Dale_, Jul 27 2019 *)

%o (Magma) [(9*n+3)^5: n in [0..30]]; // _Vincenzo Librandi_, Jul 23 2011

%Y Cf. A013663, A016781, A017197.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_