A017121 a(n) = (8*n + 4)^9.
262144, 5159780352, 512000000000, 10578455953408, 101559956668416, 618121839509504, 2779905883635712, 10077696000000000, 31087100296429568, 84590643846578176, 208215748530929664, 472161363286556672, 1000000000000000000, 1999004627104432128, 3802961274698203136
Offset: 0
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).
Programs
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Magma
[(8*n+4)^9: n in [0..15] ]; // Vincenzo Librandi, Jul 21 2011
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Mathematica
Table[(8*n + 4)^9, {n, 0, 20}] (* Amiram Eldar, Apr 25 2023 *)
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.
Sum_{n>=0} 1/a(n) = 511*zeta(9)/134217728.
Sum_{n>=0} (-1)^n/a(n) = 277*Pi^9/2164663517184. (End)