A159504 Numerator of Hermite(n, 10/13).
1, 20, 62, -12280, -308468, 10433200, 729974920, -6559031200, -1858301284720, -19430405329600, 5264344401526240, 170961658044572800, -16153599323983104320, -1016492471508449363200, 50649065999412773118080, 5823023695166237849024000, -140330290713698002728185600
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..422
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(20/13)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jun 11 2018
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Mathematica
Numerator[Table[HermiteH[n,10/13],{n,0,50}]] (* Vladimir Joseph Stephan Orlovsky, Apr 14 2011 *) -
PARI
a(n)=numerator(polhermite(n,10/13)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
From G. C. Greubel, Jun 11 2018: (Start)
a(n) = 13^n * Hermite(n,10/13).
E.g.f.: exp(20*x-169*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/13)^(n-2*k)/(k!*(n-2*k)!)). (End)