A016929 a(n) = (6*n + 1)^9.

1, 40353607, 10604499373, 322687697779, 3814697265625, 26439622160671, 129961739795077, 502592611936843, 1628413597910449, 4605366583984375, 11694146092834141, 27206534396294947, 58871586708267913, 119851595982618319, 231616946283203125, 427929800129788411

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..2000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A016921, A016922, A016923, A016924, A016925, A016926, A016927, A016928.

Programs

Magma

[(6*n+1)^9: n in [0..25]]; // Vincenzo Librandi, May 04 2011

Mathematica

(6*Range[0,20]+1)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{1,40353607,10604499373,322687697779,3814697265625,26439622160671,129961739795077,502592611936843,1628413597910449,4605366583984375},20] (* Harvey P. Dale, Mar 22 2015 *)

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, Mar 22 2015

From Amiram Eldar, Mar 28 2022: (Start)

a(n) = A016921(n)^9 = A016923(n)^3.

Sum_{n>=0} 1/a(n) = 15371*Pi^9/(529079040*sqrt(3)) + 5028751*zeta(9)/10077696. (End)