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%I #32 Sep 08 2022 08:44:41
%S 1,243,3125,16807,59049,161051,371293,759375,1419857,2476099,4084101,
%T 6436343,9765625,14348907,20511149,28629151,39135393,52521875,
%U 69343957,90224199,115856201,147008443,184528125,229345007,282475249,345025251,418195493,503284375,601692057
%N a(n) = (2*n+1)^5.
%H Vincenzo Librandi, <a href="/A016757/b016757.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.: (1+x)*(x^4 +236*x^3 +1446*x^2 +236*x +1)/(x-1)^6 . - _R. J. Mathar_, Jul 07 2017
%F From _Amiram Eldar_, Oct 10 2020: (Start)
%F Sum_{n>=0} 1/a(n) = 31*zeta(5)/32.
%F Sum_{n>=0} (-1)^n/a(n) = 5*Pi^5/1536 (A175571). (End)
%t Table[(2*n+1)^5, {n,0,30}] (* _G. C. Greubel_, Sep 15 2018 *)
%t LinearRecurrence[{6,-15,20,-15,6,-1},{1,243,3125,16807,59049,161051},30] (* _Harvey P. Dale_, Sep 04 2022 *)
%o (Magma) [(2*n+1)^5: n in [0..30]]; // _Vincenzo Librandi_, Sep 07 2011
%o (Maxima) makelist((2*n+1)^5, n, 0, 20); /* _Martin Ettl_, Nov 12 2012 */
%o (PARI) vector(30, n, n--; (2*n+1)^5) \\ _G. C. Greubel_, Sep 15 2018
%Y Cf. A175571.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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