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a(n) = (9*n + 3)^7.
1

%I #22 Dec 30 2024 22:43:13

%S 2187,35831808,1801088541,21870000000,137231006679,587068342272,

%T 1954897493193,5455160701056,13348388671875,29509034655744,

%U 60170087060757,114868566764928,207616015289871,358318080000000,594467302491009,953133216331392,1483273860320763,2248392813428736

%N a(n) = (9*n + 3)^7.

%H Vincenzo Librandi, <a href="/A017203/b017203.txt">Table of n, a(n) for n = 0..10000</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_, Oct 03 2024: (Start)

%F a(n) = A017197(n)^7 = 3^7 * A016783(n).

%F Sum_{n>=0} 1/a(n) = 28*Pi^7/(215233605*sqrt(3)) + 1093*zeta(7)/4782969. (End)

%t Table[(9*n + 3)^7, {n, 0, 20}] (* _Amiram Eldar_, Oct 03 2024 *)

%o (Magma) [(9*n+3)^7: n in [0..20]]; // _Vincenzo Librandi_, Jul 23 2011

%Y Cf. A013665, A016783, A017197.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_