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 A006750 Coefficients of Legendre polynomials. (Formerly M4564) 1

%I M4564

%S 8,88,2992,23408,354200,2641320,156641760,1159149024,17161845272,

%T 127234370120,3780912959824,28153740304144,420295123111864,

%U 3144786170643656,377374340477238720,2836750530124023744

%N Coefficients of Legendre polynomials.

%C Coefficient of Legendre_5(x) when x^n is written in term of Legendre polynomials. - _Michel Marcus_, May 28 2013

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H Vincenzo Librandi, <a href="/A006750/b006750.txt">Table of n, a(n) for n = 2..200</a>

%H H. E. Salzer, <a href="http://dx.doi.org/10.1090/S0025-5718-1948-0023123-5">Coefficients for expressing the first twenty-four powers in terms of the Legendre polynomials</a>, Math. Comp., 3 (1948), 16-18.

%t 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 *)

%o (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

%o (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

%K nonn

%O 2,1

%A _N. J. A. Sloane_.

%E More terms from _Michel Marcus_, May 29 2013

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Last modified June 23 13:59 EDT 2021. Contains 345402 sequences. (Running on oeis4.)