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A158960
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Numerator of Hermite(n, 1/5).
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10
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1, 2, -46, -292, 6316, 71032, -1436936, -24183472, 454560656, 10582510112, -183387274976, -5658029605952, 89546942024896, 3573911647620992, -51057689020940416, -2603853531376575232, 33085559702952161536, 2149253944507164508672
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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D-finite with recurrence a(n) -2*a(n-1) +50*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 5^n * Hermite(n,1/5).
E.g.f.: exp(2*x-25*x^2).
a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(2/5)^(n-2k)/(k!*(n-2k)!). (End)
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EXAMPLE
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Numerators of 1, 2/5, -46/25, -292/125, 6316/625, 71032/3125, -1436936/15625,..
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MAPLE
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orthopoly[H](n, 1/5) ;
numer(%) ;
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MATHEMATICA
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(2/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 02 2018
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CROSSREFS
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KEYWORD
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sign,frac
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AUTHOR
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STATUS
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approved
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