A016965 a(n) = (6*n + 4)^9.

262144, 1000000000, 68719476736, 1207269217792, 10578455953408, 60716992766464, 262144000000000, 922190162669056, 2779905883635712, 7427658739644928, 18014398509481984, 40353607000000000, 84590643846578176, 167619550409708032, 316478381828866048, 572994802228616704

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..1000
• Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).

Crossrefs

Cf. A016797, A016957, A016958, A016959, A016960, A016961, A016962, A016963, A016964.

Subsequence of A001017.

Programs

Magma

[(6*n+4)^9: n in [0..20]]; // Vincenzo Librandi, May 07 2011

Mathematica

(6*Range[0,20]+4)^9 (* or *) LinearRecurrence[{10,-45,120,-210,252,-210,120,-45,10,-1},{262144,1000000000,68719476736,1207269217792,10578455953408,60716992766464,262144000000000,922190162669056,2779905883635712,7427658739644928},20] (* Harvey P. Dale, Mar 04 2016 *)

Formula

From Amiram Eldar, Mar 31 2022: (Start)

a(n) = A016957(n)^9 = A016958(n)^3.

a(n) = 2^9*A016797(n).

Sum_{n>=0} 1/a(n) = 9841*zeta(9)/10077696 - 809*Pi^9/(14285134080*sqrt(3)). (End)