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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 September 23 17:43 EDT 2017. Contains 292362 sequences.