A016761 a(n) = (2*n+1)^9.

1, 19683, 1953125, 40353607, 387420489, 2357947691, 10604499373, 38443359375, 118587876497, 322687697779, 794280046581, 1801152661463, 3814697265625, 7625597484987, 14507145975869, 26439622160671, 46411484401953, 78815638671875, 129961739795077, 208728361158759

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. A016749, A258816.

Programs

Magma

[(2*n+1)^9: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011

Mathematica

(2Range[0,20]+1)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210, 120,-45, 10,-1},{1,19683,1953125,40353607,387420489,2357947691, 10604499373, 38443359375,118587876497,322687697779}, 20] (* Harvey P. Dale, Jul 25 2013 *)

PARI

vector(30, n, n--; (2*n+1)^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, Jul 25 2013

From Amiram Eldar, Oct 11 2020: (Start)

Sum_{n>=0} 1/a(n) = 511*zeta(9)/512.

Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/8257536 (A258816). (End)