A144124 P_4(2n+1), the Legendre polynomial of order 4 at 2n+1.
1, 321, 2641, 10321, 28401, 63601, 124321, 220641, 364321, 568801, 849201, 1222321, 1706641, 2322321, 3091201, 4036801, 5184321, 6560641, 8194321, 10115601, 12356401, 14950321, 17932641, 21340321, 25212001, 29588001
Offset: 0
Links
- Eric W. Weisstein, Legendre Polynomial.
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Crossrefs
Cf. A140870.
Programs
-
Magma
P
:= PolynomialRing(IntegerRing()); LP_4 :=LegendrePolynomial(4); [ Evaluate(LP_4, 2*n+1): n in [0..25] ]; // Klaus Brockhaus, Nov 21 2009 -
Mathematica
Table[LegendreP[4,2n+1],{n,0,50}] (* N. J. A. Sloane, Nov 17 2009 *) -
PARI
a(n)=pollegendre(4,n+n+1) \\ Charles R Greathouse IV, Oct 25 2011
Formula
From Klaus Brockhaus, Nov 21 2009: (Start)
a(n) = 70*n^4 + 140*n^3 + 90*n^2 + 20*n + 1.
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.
G.f.: (1 + 316*x + 1046*x^2 + 316*x^3 + x^4)/(1-x)^5. (End)
Extensions
Definition corrected by N. J. A. Sloane, Nov 17 2009
Comments