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 A006750 Coefficients of Legendre polynomials. (Formerly M4564) 1
 8, 88, 2992, 23408, 354200, 2641320, 156641760, 1159149024, 17161845272, 127234370120, 3780912959824, 28153740304144, 420295123111864, 3144786170643656, 377374340477238720, 2836750530124023744 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Coefficient of Legendre_5(x) when x^n is written in term of Legendre polynomials. - Michel Marcus, May 28 2013 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS Vincenzo Librandi, Table of n, a(n) for n = 2..200 H. E. Salzer, Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials, Math. Comp., 3 (1948), 16-18. MATHEMATICA Table[(22 n ((2 n - 2) (4 n + 1)) / ((2 n + 1) (2 n + 3) (2 n + 5) (2 n + 7))) Numerator[Binomial[4 n, 2 n] / 2^(4*n)], {n, 2, 20}] (* Vincenzo Librandi, Sep 08 2013 *) PROG (PARI) a(n) = (22*n*((2*n-2)*(4*n+1))/((2*n+1)*(2*n+3)*(2*n+5)*(2*n+7)))*numerator(binomial(4*n, 2*n)/2^(4*n)) \\ Michel Marcus, May 29 2013 (Magma) [(22*n*((2*n-2)*(4*n+1))/((2*n+1)*(2*n+3)*(2*n+5)*(2*n+7)))*Numerator(Binomial(4*n, 2*n)/2^(4*n)): n in [2..25]]; // Vincenzo Librandi, Sep 08 2013 CROSSREFS Sequence in context: A003497 A051605 A271268 * A082783 A137144 A107677 Adjacent sequences: A006747 A006748 A006749 * A006751 A006752 A006753 KEYWORD nonn AUTHOR N. J. A. Sloane. EXTENSIONS More terms from Michel Marcus, May 29 2013 STATUS approved

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Last modified November 30 03:08 EST 2023. Contains 367452 sequences. (Running on oeis4.)