%I #24 Apr 18 2023 05:02:44

%S 15625,11390625,244140625,1838265625,8303765625,27680640625,

%T 75418890625,177978515625,377149515625,735091890625,1340095640625,

%U 2313060765625,3814697265625,6053445140625,9294114390625,13867245015625,20179187015625,28722900390625,40089475140625

%N a(n) = (10*n + 5)^6.

%H Vincenzo Librandi, <a href="/A017334/b017334.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).

%F G.f.: -15625*(x^6 + 722*x^5 + 10543*x^4 + 23548*x^3 + 10543*x^2 + 722*x + 1)/(x-1)^7. - _Colin Barker_, Nov 14 2012

%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7); a(0)=15625, a(1)=11390625, a(2)=244140625, a(3)=1838265625, a(4)=8303765625, a(5)=27680640625, a(6)=75418890625. - _Harvey P. Dale_, Aug 13 2013

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

%F a(n) = A017329(n)^6.

%F a(n) = 5^6 * A016758(n).

%F Sum_{n>=0} 1/a(n) = Pi^6/15000000. (End)

%t (10*Range[0,20]+5)^6 (* or *) LinearRecurrence[{7,-21,35,-35,21,-7,1},{15625,11390625,244140625,1838265625,8303765625,27680640625,75418890625},20] (* _Harvey P. Dale_, Aug 13 2013 *)

%o (Magma) [(10*n+5)^6: n in [0..25]]; // _Vincenzo Librandi_, Aug 02 2011

%Y Cf. A016758, A017329.

%K nonn,easy

%O 0,1

%A _N. J. A. Sloane_