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a(n) = (6*n + 3)^7.
6

%I #17 Mar 30 2022 06:34:36

%S 2187,4782969,170859375,1801088541,10460353203,42618442977,

%T 137231006679,373669453125,897410677851,1954897493193,3938980639167,

%U 7446353252589,13348388671875,22876792454961,37725479487783,60170087060757,93206534790699,140710042265625,207616015289871

%N a(n) = (6*n + 3)^7.

%H Vincenzo Librandi, <a href="/A016951/b016951.txt">Table of n, a(n) for n = 0..2000</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (8,-28,56,-70,56,-28,8,-1).

%F From _Amiram Eldar_, Mar 30 2022: (Start)

%F a(n) = A016945(n)^7.

%F a(n) = 3^7*A016759(n).

%F Sum_{n>=0} 1/a(n) = 127*zeta(7)/279936.

%F Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/403107840. (End)

%t a[n_] := (6*n + 3)^7; Array[a, 50, 0] (* _Amiram Eldar_, Mar 30 2022 *)

%o (Magma) [(6*n+3)^7: n in [0..40]]; // _Vincenzo Librandi_, May 05 2011

%Y Cf. A016759, A016945, A016946, A016947, A016948, A016949, A016950.

%Y Subsequence of A001015.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_