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A159650
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Numerator of Hermite(n, 12/19).
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1
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1, 24, -146, -38160, -599604, 95815584, 4464144456, -307933642944, -29952193511280, 1059772077373824, 220063883293269216, -2370021199600548096, -1804627869905557267776, -22777205204394225722880, 16391584262028099097996416, 623630012494691211958785024
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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) - 24*a(n-1) + 722*(n-1)*a(n-2) = 0. [DLMF] - R. J. Mathar, Feb 16 2014
a(n) = 19^n * Hermite(n, 12/19).
E.g.f.: exp(24*x - 361*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(24/19)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerator of 1, 24/19, -146/361, -38160/6859, -599604/130321, 95815584/2476099, ...
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MAPLE
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orthopoly[H](n, 12/19) ;
numer(%) ;
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MATHEMATICA
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Table[19^n*HermiteH[n, 12/19], {n, 0, 50}] (* G. C. Greubel, Jul 11 2018 *)
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PROG
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(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(24/19)^(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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