A016975 a(n) = (6*n + 5)^7.

78125, 19487171, 410338673, 3404825447, 17249876309, 64339296875, 194754273881, 506623120463, 1174711139837, 2488651484819, 4902227890625, 9095120158391, 16048523266853, 27136050989627, 44231334895529, 69833729609375, 107213535210701, 160578147647843, 235260548044817

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A016969 (6*n + 5), A016970, A016971, A016972, A016973, A016974.

Subsequence of A001015 (n^7).

Programs

Magma

[(6*n+5)^7: n in [0..25]]; // Vincenzo Librandi, May 11 2011

Mathematica

(6Range[0,20]+5)^7 (* or *) LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{78125,19487171,410338673,3404825447,17249876309,64339296875,194754273881,506623120463},20] (* Harvey P. Dale, Jan 30 2013 *)

Formula

a(n) = 8*a(n-1) - 28*a(n-2) + 56*a(n-3) - 70*a(n-4) + 56*a(n-5) - 28*a(n-6) + 8*a(n-7) - a(n-8). - Harvey P. Dale, Jan 30 2013

From Amiram Eldar, Apr 01 2022: (Start)

a(n) = A016969(n)^7.

Sum_{n>=0} 1/a(n) = 138811*zeta(7)/279936 - 301*Pi^7/(1049760*sqrt(3)). (End)