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A160741
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Numerator of P_6(2n), the Legendre polynomial of order 6 at 2n.
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5
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-5, 10159, 867211, 10373071, 59271739, 227860495, 683245579, 1727242351, 3854919931, 7823790319, 14733641995, 26117017999, 44040338491, 71215667791, 111123125899, 168143944495, 247704167419, 356428995631, 502307776651, 694869638479, 945369767995
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: -(5 - 10194*x - 795993*x^2 - 4516108*x^3 - 4515933*x^4 - 796098*x^5 - 10159*x^6) / (1 - x)^7.
a(n) = 7*a(n-1) - 21*a(n-2) + 35*a(n-3) - 35*a(n-4) + 21*a(n-5) - 7*a(n-6) + a(n-7) for n>6.
a(n) = -5 + 420*n^2 - 5040*n^4 + 14784*n^6.
(End)
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MAPLE
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orthopoly[P](6, 2*n) ;
numer(%) ;
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MATHEMATICA
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Table[Numerator[LegendreP[6, 2n]], {n, 0, 40}]
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PROG
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(PARI) Vec(-(5 - 10194*x - 795993*x^2 - 4516108*x^3 - 4515933*x^4 - 796098*x^5 - 10159*x^6) / (1 - x)^7 + O(x^30)) \\ Colin Barker, Jul 23 2019
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CROSSREFS
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KEYWORD
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sign,frac,easy
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AUTHOR
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STATUS
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approved
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