A159019 Numerator of Hermite(n, 5/8).
1, 5, -7, -355, -1103, 39925, 376105, -5785075, -113172895, 915114725, 37169367385, -106989875075, -13618566694895, -27008721445675, 5530280137847945, 39751307896902125, -2455777926682502975, -32631559276626402875, 1172785395732149604025
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..450
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(5/4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 14 2018
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Mathematica
Numerator[Table[HermiteH[n,5/8],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 01 2011 *) Table[4^n*HermiteH[n, 5/8], {n,0,30}] (* G. C. Greubel, Jul 14 2018 *) -
PARI
a(n)=numerator(polhermite(n,5/8)) \\ Charles R Greathouse IV, Jan 29 2016
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PARI
x='x+O('x^30); Vec(serlaplace(exp(5*x - 16*x^2))) \\ G. C. Greubel, Jul 14 2018
Formula
From G. C. Greubel, Jul 14 2018: (Start)
a(n) = 4^n * Hermite(n, 5/8).
E.g.f.: exp(5*x - 16*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/4)^(n-2*k)/(k!*(n-2*k)!)). (End)