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%I #11 Sep 08 2022 08:45:43
%S 1,7,-1,-707,-4799,107807,1954399,-18661307,-814668799,1761841207,
%T 378933847999,1771616332493,-196012302071999,-2435055913999793,
%U 110362604948800799,2477077374441460693,-65432412090510374399,-2439688784186741175193
%N Numerator of Hermite(n, 7/10).
%H G. C. Greubel, <a href="/A159252/b159252.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jun 28 2018: (Start)
%F a(n) = 5^n * Hermite(n, 7/10).
%F E.g.f.: exp(7*x-25*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(7/5)^(n-2*k)/(k!*(n-2*k)!)). (End)
%t Numerator[Table[HermiteH[n,7/10],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 12 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,7/10)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(7/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 28 2018
%Y Cf. A159247.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009