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

0,2

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).

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)

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 *)

Prog

(Magma) [(2*n+1)^9: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011
(PARI) vector(30, n, n--; (2*n+1)^9) \\ G. C. Greubel, Sep 15 2018

Crossrefs

Cf. A016749, A258816.

Sequence in context: A186622 A250459 A250455 * A250593 A016773 A016845

Adjacent sequences: A016758 A016759 A016760 * A016762 A016763 A016764

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved