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