A017121 a(n) = (8*n + 4)^9.

262144, 5159780352, 512000000000, 10578455953408, 101559956668416, 618121839509504, 2779905883635712, 10077696000000000, 31087100296429568, 84590643846578176, 208215748530929664, 472161363286556672, 1000000000000000000, 1999004627104432128, 3802961274698203136

Offset

0,1

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).

Formula

G.f.: 262144*(1+x)*(x^8 + 19672*x^7 + 1736668*x^6 + 19971304*x^5 + 49441990*x^4 + 19971304*x^3 + 1736668*x^2 + 19672*x + 1) / (x-1)^10 . - R. J. Mathar, May 08 2015

From Amiram Eldar, Apr 25 2023: (Start)

a(n) = A017113(n)^9.

a(n) = 2^9*A016833(n) = 2^18*A016761(n).

Sum_{n>=0} 1/a(n) = 511*zeta(9)/134217728.

Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/2164663517184. (End)

Mathematica

Table[(8*n + 4)^9, {n, 0, 20}] (* Amiram Eldar, Apr 25 2023 *)

Prog

(Magma) [(8*n+4)^9: n in [0..15] ]; // Vincenzo Librandi, Jul 21 2011

Crossrefs

Cf. A013667, A016761, A016833, A017113.

Sequence in context: A183818 A016965 A017037 * A017217 A017325 A017445

Adjacent sequences: A017118 A017119 A017120 * A017122 A017123 A017124

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved