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A159997
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Numerator of Hermite(n, 19/24).
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1
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1, 19, 73, -9557, -244655, 6361219, 473166361, -2002025573, -991941869663, -14234228603405, 2300662982701801, 84707175049140619, -5679064003265633807, -400650213031877021597, 13650061580620869563065, 1874772828976324672777339, -23347582277731987729671359
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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) = 12^n * Hermite(n, 19/24).
E.g.f.: exp(19*x - 144*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(19/12)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 19/12, 73/144, -9557/1728, -244655/20736, ...
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MATHEMATICA
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Numerator[HermiteH[Range[0, 20], 19/24]] (* Harvey P. Dale, Jun 12 2016 *)
Table[12^n*HermiteH[n, 19/12], {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(19*x - 144*x^2))) \\ G. C. Greubel, Jul 16 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(19/12)^(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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