A159538 Numerator of Hermite(n, 10/17).
1, 20, -178, -26680, -224948, 57185200, 1793803720, -162442199200, -10506573835120, 541001252398400, 65475222138262240, -1817482796097507200, -452641118277021465920, 3553238308191880620800, 3472210128897376907338880, 40691398188058840163264000
Offset: 0
Links
- G. C. Greubel, Table of n, a(n) for n = 0..404
Programs
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Magma
[Numerator((&+[(-1)^k*Factorial(n)*(20/17)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // G. C. Greubel, Jul 02 2018
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Mathematica
Numerator[Table[HermiteH[n,10/17],{n,0,30}]] (* Vladimir Joseph Stephan Orlovsky, May 08 2011 *) Table[17^n*HermiteH[n, 10/17], {n,0,30}] (* G. C. Greubel, Jul 02 2018 *) -
PARI
a(n)=numerator(polhermite(n,10/17)) \\ Charles R Greathouse IV, Jan 29 2016
Formula
From G. C. Greubel, Jul 02 2018: (Start)
a(n) = 17^n * Hermite(n, 10/17).
E.g.f.: exp(20*x-289*x^2).
a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(20/17)^(n-2*k)/(k!*(n-2*k)!)). (End)