A016746 a(n) = (2*n)^6.

0, 64, 4096, 46656, 262144, 1000000, 2985984, 7529536, 16777216, 34012224, 64000000, 113379904, 191102976, 308915776, 481890304, 729000000, 1073741824, 1544804416, 2176782336, 3010936384, 4096000000, 5489031744, 7256313856, 9474296896, 12230590464, 15625000000

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 (7,-21,35,-35,21,-7,1).

Crossrefs

Cf. A016758.

Programs

Magma

[(2*n)^6: n in [0..30]]; // Vincenzo Librandi, Sep 05 2011

Maple

A016746:=n->(2*n)^6: seq(A016746(n), n=0..50); # Wesley Ivan Hurt, Sep 15 2018

Mathematica

Table[(2*n)^6, {n,0,30}] (* G. C. Greubel, Sep 15 2018 *)

PARI

vector(30, n, n--; (2*n)^6) \\ G. C. Greubel, Sep 15 2018

Formula

G.f.: 64*x*(1+x)*(x^4 + 56*x^3 + 246*x^2 + 56*x + 1) / (1-x)^7. - R. J. Mathar, May 01 2015

E.g.f.: 64*x*(1 + 31*x + 90*x^2 + 65*x^3 + 15*x^4 + x^5)*exp(x). - G. C. Greubel, Sep 15 2018

From Amiram Eldar, Oct 10 2020: (Start)

Sum_{n>=1} 1/a(n) = Pi^6/60480.

Sum_{n>=1} (-1)^(n+1)/a(n) = 31*Pi^6/1935360. (End)