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

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

Offset

0,2

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).

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)

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 *)

Prog

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

Crossrefs

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

Sequence in context: A186960 A186571 A186572 * A016989 A017157 A017253

Adjacent sequences: A016926 A016927 A016928 * A016930 A016931 A016932

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved