A017334 a(n) = (10*n + 5)^6.
15625, 11390625, 244140625, 1838265625, 8303765625, 27680640625, 75418890625, 177978515625, 377149515625, 735091890625, 1340095640625, 2313060765625, 3814697265625, 6053445140625, 9294114390625, 13867245015625, 20179187015625, 28722900390625, 40089475140625
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
-
Magma
[(10*n+5)^6: n in [0..25]]; // Vincenzo Librandi, Aug 02 2011
-
Mathematica
(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 *)
Formula
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
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
From Amiram Eldar, Apr 18 2023: (Start)
a(n) = A017329(n)^6.
a(n) = 5^6 * A016758(n).
Sum_{n>=0} 1/a(n) = Pi^6/15000000. (End)