|
%I #19 Sep 08 2022 08:45:12
%S 42,462,1586,3958,8330,15694,27314,44758,69930,105102,152946,216566,
%T 299530,405902,540274,707798,914218,1165902,1469874,1833846,2266250,
%U 2776270,3373874,4069846,4875818,5804302,6868722,8083446,9463818
%N a(n) = K_5(n) = Sum_{k>=0} A090285(5,k)*2^k*binomial(n,k). a(n) = 2*(2*n^5+45*n^4+360*n^3+1215*n^2+1528*n+315)/15.
%C Values of polynomial K_5 related to A090285.
%H Vincenzo Librandi, <a href="/A090297/b090297.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).
%F G.f.: (42+210*x-556*x^2+532*x^3-238*x^4+42*x^5)/(1-x)^6. [_Colin Barker_, Sep 18 2012]
%t Table[(2*(2*n^5 + 45*n^4 + 360*n^3 + 1215*n^2 + 1528*n + 315)/15),{n, 0, 50}] (* _Vincenzo Librandi_, Sep 18 2012 *)
%t LinearRecurrence[{6,-15,20,-15,6,-1},{42,462,1586,3958,8330,15694},30] (* _Harvey P. Dale_, Apr 17 2020 *)
%o (Magma) [2*(2*n^5 + 45*n^4 + 360*n^3 + 1215*n^2 + 1528*n + 315)/15: n in [0..30]]; // _Vincenzo Librandi_, Sep 18 2012
%Y Cf. A090285.
%K easy,nonn
%O 0,1
%A _Philippe Deléham_, Jan 25 2004
%E Corrected by _T. D. Noe_, Nov 09 2006
|
