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A159652
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Numerator of Hermite(n, 14/19).
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1
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1, 28, 62, -38696, -1217780, 77656208, 6570559624, -152431023584, -37475677000048, -168877363780160, 238788382960467424, 7905369289385843072, -1675106997369228675392, -115395115449577347286784, 12491491044719414623199360, 1516175576216471435824394752
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OFFSET
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0,2
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LINKS
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FORMULA
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D-finite with recurrence a(n) -28*a(n-1) +722*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 19^n * Hermite(n, 14/19).
E.g.f.: exp(28*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(28/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 28/19, 62/361, -38696/6859, -1217780/130321, 77656208/2476099, ...
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MAPLE
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orthopoly[H](n, 14/19) ;
numer(%) ;
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MATHEMATICA
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Table[19^n*HermiteH[n, 14/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(28/19)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 11 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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