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a(n) = (6*n + 4)^5.
8

%I #19 Jan 01 2025 12:05:38

%S 1024,100000,1048576,5153632,17210368,45435424,102400000,205962976,

%T 380204032,656356768,1073741824,1680700000,2535525376,3707398432,

%U 5277319168,7339040224,10000000000,13382255776,17623416832,22877577568,29316250624,37129300000,46525874176

%N a(n) = (6*n + 4)^5.

%H Vincenzo Librandi, <a href="/A016961/b016961.txt">Table of n, a(n) for n = 0..3000</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 From _Amiram Eldar_, Mar 31 2022: (Start)

%F a(n) = A016957(n)^5.

%F a(n) = 32*A016793(n).

%F Sum_{n>=0} 1/a(n) = 121*zeta(5)/7776 - Pi^5/(11664*sqrt(3)). (End)

%t a[n_] := (6*n + 4)^5; Array[a, 20, 0] (* _Amiram Eldar_, Mar 31 2022 *)

%t LinearRecurrence[{6,-15,20,-15,6,-1},{1024,100000,1048576,5153632,17210368,45435424},30] (* _Harvey P. Dale_, Jan 01 2025 *)

%o (Magma) [(6*n+4)^5: n in [0..30]]; // _Vincenzo Librandi_, May 06 2011

%Y Cf. A016793, A016957, A016958, A016959, A016960.

%Y Subsequence of A000584.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_