A016748 a(n) = (2*n)^8.

0, 256, 65536, 1679616, 16777216, 100000000, 429981696, 1475789056, 4294967296, 11019960576, 25600000000, 54875873536, 110075314176, 208827064576, 377801998336, 656100000000, 1099511627776, 1785793904896, 2821109907456, 4347792138496, 6553600000000, 9682651996416

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..10000
• Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).

Crossrefs

Cf. A001016, A005843, A016760.

Programs

Magma

[(2*n)^8: n in [0..20]]; // Vincenzo Librandi, Sep 05 2011

Maple

A016748:=n->(2*n)^8; seq(A016748(n), n=0..50); # Wesley Ivan Hurt, Nov 15 2013

Mathematica

Table[(2n)^8, {n,0,50}] (* Wesley Ivan Hurt, Nov 15 2013 *)
(2*Range[0,20])^8 (* or *) LinearRecurrence[{9,-36,84,-126,126,-84,36, -9, 1}, {0,256 ,65536, 1679616, 16777216, 100000000, 429981696, 1475789056, 4294967296}, 20] (* Harvey P. Dale, Jun 14 2016 *)

PARI

vector(30, n, n--; (2*n)^8) \\ G. C. Greubel, Sep 15 2018

Formula

a(n) = 256*A001016(n) = A001016(A005843(n)). - Michel Marcus, Nov 16 2013

G.f.: 256*x*(1+x)*(x^6 + 246*x^5 + 4047*x^4 + 11572*x^3 + 4047*x^2 + 246*x + 1) / (1-x)^9. - R. J. Mathar, May 01 2015

From Amiram Eldar, Oct 11 2020: (Start)

Sum_{n>=1} 1/a(n) = Pi^8/2419200.

Sum_{n>=1} (-1)^(n+1)/a(n) = 127*Pi^8/309657600. (End)