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A159884
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Numerator of Hermite(n, 15/23).
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1
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1, 30, -158, -68220, -1545108, 242353800, 15444235320, -1075134862800, -146634052663920, 4700919898821600, 1537277046430494240, -3617421136617700800, -17999352900456622989120, -494053808263200360316800, 232741485544984381782852480, 14300169574344055190498016000
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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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a(n) = 23^n * Hermite(n, 15/23).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(30/23)^(n-2*k)/(k!*(n-2*k)!)). (End)
D-finite with recurrence a(n) -30*a(n-1) +1058*(n-1)*a(n-2)=0. [DLMF] - R. J. Mathar, Feb 06 2021
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EXAMPLE
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Numerators of 1, 30/23, -158/529, -68220/12167, -1545108/279841, ...
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 15/23 ]] (* Harvey P. Dale, Nov 16 2014 *)
Table[23^n*HermiteH[n, 15/23], {n, 0, 30}] (* G. C. Greubel, Jul 16 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(30*x - 529*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(30/23)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 16 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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