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%I #36 Sep 08 2022 08:45:32
%S 0,0,48,648,3840,15000,45360,115248,258048,524880,990000,1756920,
%T 2965248,4798248,7491120,11340000,16711680,24054048,33907248,46915560,
%U 63840000,85571640,113145648,147756048,190771200,243750000,308458800,386889048,481275648
%N a(n) = n^6 - n^4.
%H Vincenzo Librandi, <a href="/A136038/b136038.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (7,-21,35,-35,21,-7,1).
%F From _R. J. Mathar_, Feb 06 2010: (Start)
%F a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7).
%F G.f.: 24*x^2*(1+x)*(2*x^2+11*x+2)/(1-x)^7. (End)
%F From _Amiram Eldar_, Jan 12 2021: (Start)
%F Sum_{n>=2} 1/a(n) = 11/4 - Pi^2/6 - Pi^4/90 = 11/4 - A013661 - A013662.
%F Sum_{n>=2} (-1)^n/a(n) = 7*Pi^4/720 + Pi^2/12 - 7/4 = A267315 + A072691 - 7/4. (End)
%p map(n -> n^6 - n^4, [$0..100]); # _Robert Israel_, Aug 28 2018
%t a[n_]:=n^6-n^4; a[Range[0,60]] (* _Vladimir Joseph Stephan Orlovsky_, Feb 10 2011 *)
%t LinearRecurrence[{7,-21,35,-35,21,-7,1},{0,0,48,648,3840,15000,45360},30] (* _Harvey P. Dale_, May 17 2018 *)
%o (Magma) [n^6-n^4: n in [0..30]]; // _Vincenzo Librandi_, Feb 20 2012
%Y Cf. A013661, A013662, A072691, A267315.
%K nonn,easy
%O 0,3
%A _Rolf Pleisch_, Mar 16 2008
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