A024004 a(n) = 1 - n^6.
1, 0, -63, -728, -4095, -15624, -46655, -117648, -262143, -531440, -999999, -1771560, -2985983, -4826808, -7529535, -11390624, -16777215, -24137568, -34012223, -47045880, -63999999, -85766120, -113379903, -148035888, -191102975, -244140624, -308915775, -387420488, -481890303
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..500
- Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
Programs
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Haskell
a024004 = (1 -) . (^ 6) -- Reinhard Zumkeller, Mar 11 2014
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Magma
[1-n^6: n in [0..50]]; // Vincenzo Librandi, Apr 29 2011
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Mathematica
Table[1-n^6,{n,0,40}] (* Vladimir Joseph Stephan Orlovsky, Apr 15 2011 *) -
Maxima
A024004(n):=1-n^6 $ makelist(A024004(n),n,0,30); /* Martin Ettl, Nov 05 2012 */
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PARI
for(n=0,50, print1(1-n^6, ", ")) \\ G. C. Greubel, May 11 2017
Formula
From G. C. Greubel, May 11 2017: (Start)
G.f.: (1 - 7*x - 42*x^2 - 322*x^3 - 287*x^4 - 63*x^5)/(1 - x)^7.
E.g.f.: (1 - x - 31*x^2 - 90*x^3 - 65*x^4 - 15*x^5 - x^6)*exp(x). (End)
Sum_{k>=2} -1/a(k) = 11/12 - Pi*tanh(sqrt(3)*Pi/2)/(2*sqrt(3)) = A339529. - Vaclav Kotesovec, Dec 08 2020