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%I #16 Sep 08 2022 08:45:38
%S 1,321,2641,10321,28401,63601,124321,220641,364321,568801,849201,
%T 1222321,1706641,2322321,3091201,4036801,5184321,6560641,8194321,
%U 10115601,12356401,14950321,17932641,21340321,25212001,29588001
%N P_4(2n+1), the Legendre polynomial of order 4 at 2n+1.
%C Legendre polynomial LP_4(x) = (35*x^4 - 30*x^2 + 3)/8. - _Klaus Brockhaus_, Nov 21 2009
%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/LegendrePolynomial.html">Legendre Polynomial.</a>
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F From _Klaus Brockhaus_, Nov 21 2009: (Start)
%F a(n) = 70*n^4 + 140*n^3 + 90*n^2 + 20*n + 1.
%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3) - a(n-4) + 1680 for n > 3; a(0)=1, a(1)=321, a(2)=2641, a(3)=10321.
%F G.f.: (1 + 316*x + 1046*x^2 + 316*x^3 + x^4)/(1-x)^5. (End)
%t Table[LegendreP[4,2n+1],{n,0,50}] (* _N. J. A. Sloane_, Nov 17 2009 *)
%o (Magma) P<x> := PolynomialRing(IntegerRing()); LP_4<x>:=LegendrePolynomial(4); [ Evaluate(LP_4, 2*n+1): n in [0..25] ]; // _Klaus Brockhaus_, Nov 21 2009
%o (PARI) a(n)=pollegendre(4,n+n+1) \\ _Charles R Greathouse IV_, Oct 25 2011
%Y Cf. A140870.
%K nonn,easy
%O 0,2
%A _Vladimir Joseph Stephan Orlovsky_, Sep 11 2008
%E Definition corrected by _N. J. A. Sloane_, Nov 17 2009
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