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A160286
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Numerator of Hermite(n, 24/29).
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1
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1, 48, 622, -131616, -9456180, 431615808, 100244032584, 455846829696, -1158392591818608, -61736719347682560, 14572384526261325024, 1737886076688564260352, -186199726823835951097152, -44015079459426106683608064, 1958719412677543785877138560
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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) = 29^n * Hermite(n, 24/29).
E.g.f.: exp(48*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(48/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 48/29, 622/841, -131616/24389, -9456180/707281, ...
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MATHEMATICA
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Table[29^n*HermiteH[n, 24/29], {n, 0, 30}] (* G. C. Greubel, Oct 03 2018 *)
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PROG
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(PARI) x='x+O('x^30); Vec(serlaplace(exp(48*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(48/29)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Oct 03 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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