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 A144124 P_4(2n+1), the Legendre polynomial of order 4 at 2n+1. 2
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Legendre polynomial LP_4(x) = (35*x^4 - 30*x^2 + 3)/8. - Klaus Brockhaus, Nov 21 2009 LINKS Eric W. Weisstein, Legendre Polynomial. Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1). 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) MATHEMATICA Table[LegendreP[4, 2n+1], {n, 0, 50}] (* N. J. A. Sloane, Nov 17 2009 *) PROG (MAGMA) P := PolynomialRing(IntegerRing()); LP_4:=LegendrePolynomial(4); [ Evaluate(LP_4, 2*n+1): n in [0..25] ]; // Klaus Brockhaus, Nov 21 2009 (PARI) a(n)=pollegendre(4, n+n+1) \\ Charles R Greathouse IV, Oct 25 2011 CROSSREFS Cf. A140870. Sequence in context: A228226 A004927 A074350 * A090101 A105952 A062205 Adjacent sequences:  A144121 A144122 A144123 * A144125 A144126 A144127 KEYWORD nonn,easy AUTHOR Vladimir Joseph Stephan Orlovsky, Sep 11 2008 EXTENSIONS Definition corrected by N. J. A. Sloane, Nov 17 2009 STATUS approved

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Last modified April 18 10:56 EDT 2021. Contains 343087 sequences. (Running on oeis4.)