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A144124
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P_4(2n+1), the Legendre polynomial of order 4 at 2n+1.
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1
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1, 321, 2641, 10321, 28401, 63601, 124321, 220641, 364321, 568801, 849201, 1222321, 1706641, 2322321, 3091201, 4036801, 5184321, 6560641, 8194321, 10115601, 12356401, 14950321, 17932641, 21340321, 25212001, 29588001
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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]
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LINKS
| Eric W. Weisstein, Legendre Polynomial.
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
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FORMULA
| Contribution from Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 21 2009: (Start)
a(n) = 70*n^4+140*n^3+90*n^2+20*n+1.
a(n) = 4*a(n-1)-6*a(n-2)+4*a(n-3)-a(n-4)+1680 for n > 3; a(0)=1, a(1)=321, a(2)=2641, a(3)=10321.
G.f.: (1+316*x+1046*x^2+316*x^3+x^4)/(1-x)^5. (End)
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MATHEMATICA
| Table[LegendreP[4, 2n+1], {n, 0, 50}] - N. J. A. Sloane, Nov 17 2009
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PROG
| (MAGMA) P<x> := PolynomialRing(IntegerRing()); LP_4<x>:=LegendrePolynomial(4); [ Evaluate(LP_4, 2*n+1): n in [0..25] ]; [From Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Nov 21 2009]
(PARI) a(n)=pollegendre(4, n+n+1) \\ Charles R Greathouse IV, Oct 25 2011
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CROSSREFS
| Cf. A140870.
Sequence in context: A174778 A004927 A074350 * A090101 A105952 A062205
Adjacent sequences: A144121 A144122 A144123 * A144125 A144126 A144127
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KEYWORD
| nonn,easy
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AUTHOR
| Vladimir Orlovsky (4vladimir(AT)gmail.com), Sep 11 2008
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EXTENSIONS
| Definition corrected by N. J. A. Sloane, Nov 17 2009
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