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A160280
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Numerator of Hermite(n, 18/29).
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1
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1, 36, -386, -135000, -2912244, 803439216, 53415783816, -6185340350496, -851589691267440, 52572710870646336, 14783982337749774816, -352049632685279478144, -286207027989716394858816, -3197683221510109228058880, 6143086278048774757772750976
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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, 18/29).
E.g.f.: exp(36*x - 841*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(36/29)^(n-2*k)/(k!*(n-2*k)!)). (End)
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EXAMPLE
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Numerators of 1, 36/29, -386/841, -135000/24389, -2912244/707281, ...
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MATHEMATICA
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Table[29^n*HermiteH[n, 18/29], {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(36*x - 841*x^2))) \\ G. C. Greubel, Oct 03 2018
(Magma) [Numerator((&+[(-1)^k*Factorial(n)*(36/29)^(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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