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%I #20 Aug 03 2023 19:39:00
%S 0,1,362,3363,15124,47525,120126,262087,514088,930249,1580050,2550251,
%T 3946812,5896813,8550374,12082575,16695376,22619537,30116538,39480499,
%U 51040100,65160501,82245262,102738263,127125624,155937625,189750626,229188987
%N a(n) = 16*n^5 - 20*n^3 + 5*n.
%C Chebyshev polynomial of the first kind T(5,n).
%H Vincenzo Librandi, <a href="/A243131/b243131.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 a(n) = n*(16*n^4-20*n^2+5) = (-1/4)*n *(-8*n^2+5+sqrt(5))*(8*n^2-5+sqrt(5)).
%F G.f.: x*(1 + 356*x + 1206*x^2 + 356*x^3 + x^4)/(1 - x)^6.
%p a:= n-> simplify(ChebyshevT(5, n)):
%p seq(a(n), n=0..30); # _Alois P. Heinz_, May 31 2014
%t Table[ChebyshevT[5, n], {n, 0, 40}] (* or *) Table[16*n^5 - 20*n^3 + 5*n, {n, 0, 20}]
%t LinearRecurrence[{6,-15,20,-15,6,-1},{0,1,362,3363,15124,47525},30] (* _Harvey P. Dale_, Aug 03 2023 *)
%o (Magma) [16*n^5-20*n^3+5*n: n in [0..40]];
%o (PARI) apply(x->polchebyshev(5,1,x), vector(30,i,i-1)) \\ _Hugo Pfoertner_, Oct 18 2022
%Y Cf. A056220, A144129, A144130.
%K nonn,easy
%O 0,3
%A _Vincenzo Librandi_, May 31 2014
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