%I #12 Sep 08 2022 08:45:43
%S 1,5,-73,-1345,14737,600925,-4216505,-374426425,1020390305,
%T 298652268725,593277094615,-289712837877425,-2088116897382095,
%U 330261712856941325,4311569491549495655,-431561222581976019625,-8495813265487638710975,634208930681100205217125
%N Numerator of Hermite(n, 5/14).
%H G. C. Greubel, <a href="/A159509/b159509.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jun 11 2018: (Start)
%F a(n) = 7^n * Hermite(n,5/14).
%F E.g.f.: exp(5*x-49*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(5/7)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,5/14],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 14 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,5/14)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(5/7)^(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
%Y Cf. A159507.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009