A016749 a(n) = (2*n)^9.

0, 512, 262144, 10077696, 134217728, 1000000000, 5159780352, 20661046784, 68719476736, 198359290368, 512000000000, 1207269217792, 2641807540224, 5429503678976, 10578455953408, 19683000000000, 35184372088832, 60716992766464, 101559956668416, 165216101262848

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 (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A016761.

Programs

Magma

[(2*n)^9: n in [0..20]]; // Vincenzo Librandi, Sep 05 2011

Maple

A016749:=n->(2*n)^9: seq(A016749(n), n=0..30); # Wesley Ivan Hurt, Sep 15 2018

Mathematica

Table[(2n)^9, {n, 0, 40}] (* Stefan Steinerberger, Apr 08 2006 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45, 10, -1}, {0,512, 262144, 10077696, 134217728, 1000000000, 5159780352, 20661046784, 68719476736, 198359290368}, 20] (* Harvey P. Dale, Jan 13 2013 *)

PARI

vector(30, n, n--; (2*n)^9) \\ G. C. Greubel, Sep 15 2018

Formula

a(n) = 10*a(n-1)-45*a(n-2)+ 120*a(n-3)- 210*a(n-4)+252*a(n-5)-210*a(n-6)+120*a(n-7)-45*a(n-8)+10*a(n-9)-a(n-10). - Harvey P. Dale, Jan 13 2013

From Amiram Eldar, Oct 11 2020: (Start)

Sum_{n>=1} 1/a(n) = zeta(9)/512.

Sum_{n>=1} (-1)^(n+1)/a(n) = 255*zeta(9)/131072. (End)

Extensions

More terms from Stefan Steinerberger, Apr 08 2006