A016759 a(n) = (2*n + 1)^7.

1, 2187, 78125, 823543, 4782969, 19487171, 62748517, 170859375, 410338673, 893871739, 1801088541, 3404825447, 6103515625, 10460353203, 17249876309, 27512614111, 42618442977, 64339296875, 94931877133, 137231006679, 194754273881, 271818611107, 373669453125, 506623120463

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Philippe A. J. G. Chevalier, On the discrete geometry of physical quantities, Preprint, 2012.
• Philippe A. J. G. Chevalier, A "table of Mendeleev" for physical quantities?, Slides from a talk, May 14 2014, Leuven, Belgium.
• Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).

Crossrefs

Cf. A001015, A005408, A215960, A258814.

Programs

Magma

[(2*n+1)^7: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011

Mathematica

Table[(2*n+1)^7, {n,0,30}] (* G. C. Greubel, Sep 15 2018 *)
LinearRecurrence[{8,-28,56,-70,56,-28,8,-1},{1,2187,78125,823543,4782969,19487171,62748517,170859375},20] (* Harvey P. Dale, Jul 09 2019 *)

PARI

a(n) = (2*n+1)^7; \\ Michel Marcus, Mar 07 2016

Formula

a(n) = A001015(A005408(n)). - Michel Marcus, Mar 07 2016

G.f.: (1+x)*(x^6 + 2178*x^5 + 58479*x^4 + 201244*x^3 + 58479*x^2 + 2178*x + 1)/(x-1)^8. - R. J. Mathar, Jul 07 2017

From Amiram Eldar, Oct 10 2020: (Start)

Sum_{n>=0} 1/a(n) = 127*zeta(7)/128.

Sum_{n>=0} (-1)^n/a(n) = 61*Pi^7/184320 (A258814). (End)