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Coefficients of Legendre polynomials.
(Formerly M2149 N0856)
0

%I M2149 N0856 #20 Oct 12 2017 03:51:23

%S 2,28,182,4760,31654,428260,2941470,163761840,1152562950,16381761396,

%T 117402623338,3390322778024,24634522766126,360043025043380,

%U 2644479279859438,312191499849352032,2312918756095439814,34398444513178377492

%N Coefficients of Legendre polynomials.

%C Coefficient of Legendre_3(x) when x^n is written in term of Legendre polynomials. - _Sean A. Irvine_, Nov 28 2012

%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

%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.

%p a:=n->(14*n/((2*n+3)*(2*n+5)))*numer(binomial(4*n+2,2*n+1)/2^(4*n)); # _Sean A. Irvine_, Nov 28 2012

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Sean A. Irvine_, Nov 28 2012