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

0,1

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).

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)

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 *)

Prog

(Magma) [(10*n+5)^6: n in [0..25]]; // Vincenzo Librandi, Aug 02 2011

Crossrefs

Cf. A016758, A017329.

Sequence in context: A303155 A017226 A223232 * A265934 A017454 A223262

Adjacent sequences: A017331 A017332 A017333 * A017335 A017336 A017337

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved