%I #22 Apr 18 2023 05:02:32

%S 78125,170859375,6103515625,64339296875,373669453125,1522435234375,

%T 4902227890625,13348388671875,32057708828125,69833729609375,

%U 140710042265625,266001988046875,476837158203125,817215093984375,1347646586640625,2149422977421875,3329565857578125

%N a(n) = (10*n + 5)^7.

%H Vincenzo Librandi, <a href="/A017335/b017335.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 G.f.: 78125*(x+1)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1)/(x-1)^8. - _Colin Barker_, Nov 13 2012

%F From _Amiram Eldar_, Apr 18 2023: (Start)

%F a(n) = A017329(n)^7.

%F a(n) = 5^7 * A016759(n).

%F Sum_{n>=0} 1/a(n) = 127*zeta(7)/10000000.

%F Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/14400000000. (End)

%t Table[(10*n + 5)^7, {n, 0, 20}] (* _Amiram Eldar_, Apr 18 2023 *)

%o (Magma) [(10*n+5)^7: n in [0..25]]; // _Vincenzo Librandi_, Aug 02 2011

%Y Cf. A013665, A016759, A017329.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_