A016785 a(n) = (3*n + 1)^9.

1, 262144, 40353607, 1000000000, 10604499373, 68719476736, 322687697779, 1207269217792, 3814697265625, 10578455953408, 26439622160671, 60716992766464, 129961739795077, 262144000000000, 502592611936843, 922190162669056, 1628413597910449, 2779905883635712

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. A016777, A016778, A016779, A016780, A016781, A016782, A016783, A016784.

Programs

Magma

[(3*n+1)^9 : n in [0..20]]; // Vincenzo Librandi, Sep 28 2011

Maple

A016785:=n->(3*n+1)^9; seq(A016785(k), k=0..100); # Wesley Ivan Hurt, Nov 05 2013

Mathematica

Table[(3*n+1)^9, {n,0,100}] (* Wesley Ivan Hurt, Nov 05 2013 *)
LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,262144,40353607,1000000000,10604499373,68719476736,322687697779,1207269217792,3814697265625,10578455953408},100] (* Harvey P. Dale, Aug 17 2014 *)

Formula

From Amiram Eldar, Mar 29 2022: (Start)

a(n) = A016777(n)^9 = A016779(n)^3.

Sum_{n>=0} 1/a(n) = 1618*Pi^9/(55801305*sqrt(3)) + 9841*zeta(9)/3^9. (End)