A016841 a(n) = (4n+3)^5.

243, 16807, 161051, 759375, 2476099, 6436343, 14348907, 28629151, 52521875, 90224199, 147008443, 229345007, 345025251, 503284375, 714924299, 992436543, 1350125107, 1804229351, 2373046875, 3077056399, 3939040643, 4984209207, 6240321451, 7737809375, 9509900499, 11592740743

Offset

0,1

Links

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).

Formula

a(0)=243, a(1)=16807, a(2)=161051, a(3)=759375, a(4)=2476099, a(5)=6436343, a(n)=6*a(n-1)-15*a(n-2)+20*a(n-3)-15*a(n-4)+6*a(n-5)-a(n-6). - Harvey P. Dale, Aug 11 2014

From Amiram Eldar, Apr 24 2023: (Start)

a(n) = A004767(n)^5.

Sum_{n>=0} 1/a(n) = 31*zeta(5)/64 - 5*Pi^5/3072. (End)

Mathematica

(4*Range[0, 30]+3)^5 (* or *) LinearRecurrence[{6, -15, 20, -15, 6, -1}, {243, 16807, 161051, 759375, 2476099, 6436343}, 30] (* Harvey P. Dale, Aug 11 2014 *)

Crossrefs

Cf. A004767, A013663.

Sequence in context: A224313 A224377 A233024 * A128833 A223478 A231860

Adjacent sequences: A016838 A016839 A016840 * A016842 A016843 A016844

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved