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Search: id:A140870
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| A140870 |
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8*LegendreP[4,2n] (using Mma's notation). |
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+0
2
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| 3, 443, 8483, 44283, 141443, 347003, 721443, 1338683, 2286083, 3664443, 5588003, 8184443, 11594883, 15973883, 21489443, 28323003, 36669443, 46737083, 58747683, 72936443, 89552003, 108856443, 131125283, 156647483, 185725443, 218675003, 255825443
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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I would like to know how to compute this in Maple!
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LINKS
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Eric W. Weisstein, Legendre Polynomial. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 21 2009]
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FORMULA
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Legendre polynomial LP_4(x) = (35*x^4-30*x^2+3)/8. [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 21 2009]
Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 21 2009: (Start)
a(n) = 560*n^4-120*n^2+3.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4)+13440 for n > 3; a(0)=3, a(1)=443, a(2)=8483, a(3)=44283.
G.f.: (3+428*x+6298*x^2+6268*x^3+443*x^4)/(1-x)^5. (End)
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MATHEMATICA
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Table[8 LegendreP[4, 2n], {n, 0, 50}]
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PROGRAM
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(MAGMA code from Klaus Brockhaus, Nov 18 2009)
P<x> := PolynomialRing(IntegerRing());
LP4:=LegendrePolynomial(4);
[ Evaluate(8*LP4, 2*n): n in [0..26] ];
(PARI) {for(n=0, 26, print1(subst(8*pollegendre(4), x, 2*n), ", "))} [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 21 2009]
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CROSSREFS
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Cf. A144124.
Adjacent sequences: A140867 A140868 A140869 this_sequence A140871 A140872 A140873
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KEYWORD
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nonn,new
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Nov 17 2009
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