A016760 a(n) = (2*n+1)^8.
1, 6561, 390625, 5764801, 43046721, 214358881, 815730721, 2562890625, 6975757441, 16983563041, 37822859361, 78310985281, 152587890625, 282429536481, 500246412961, 852891037441, 1406408618241, 2251875390625, 3512479453921, 5352009260481, 7984925229121, 11688200277601
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
Programs
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Magma
[(2*n+1)^8: n in [0..30]]; // Vincenzo Librandi, Sep 07 2011
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Mathematica
Table[(2*n+1)^8, {n,0,30}] (* G. C. Greubel, Sep 15 2018 *) -
Maxima
A016760(n):=(2*n+1)^8$ makelist(A016760(n),n,0,20); /* Martin Ettl, Nov 12 2012 */
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PARI
vector(30, n, n--; (2*n+1)^8) \\ G. C. Greubel, Sep 15 2018
Formula
a(n) = A016756(n)^2. - Michel Marcus, Dec 26 2016
G.f.: -(1+6552*x +331612*x^2 +2485288*x^3 +4675014*x^4 +2485288*x^5 +331612*x^6 +6552*x^7 +x^8)/(x-1)^9 . - R. J. Mathar, Jul 07 2017
Sum_{n>=0} 1/a(n) = 17*Pi^8/161280 (A300710). - Amiram Eldar, Oct 11 2020
Product_{n>=1} (1 - 1/a(n)) = Pi*cosh(Pi/2)*(cos(Pi/sqrt(2)) + cosh(Pi/sqrt(2)))/32. - Amiram Eldar, Jan 28 2021