A016764 a(n) = (2*n+1)^12.

1, 531441, 244140625, 13841287201, 282429536481, 3138428376721, 23298085122481, 129746337890625, 582622237229761, 2213314919066161, 7355827511386641, 21914624432020321, 59604644775390625, 150094635296999121, 353814783205469041, 787662783788549761, 1667889514952984961

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 (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).

Crossrefs

Cf. A016752.

Programs

Magma

[(2*n+1)^12: n in [0..20]]; // Vincenzo Librandi, Sep 07 2011

Mathematica

(2*Range[0,20]+1)^12 (* Harvey P. Dale, Mar 06 2017 *)

PARI

vector(20, n, n--; (2*n+1)^12) \\ G. C. Greubel, Sep 15 2018

Formula

Sum_{n>=0} 1/a(n) = 691*Pi^12/638668800. - Amiram Eldar, Oct 11 2020

Product_{n>=1} (1 - 1/a(n)) = Pi*cosh(Pi/2)*cosh(sqrt(3)*Pi/2)*(cos(sqrt(3)*Pi/2) + cosh(Pi/2))/96. - Amiram Eldar, Jan 28 2021