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%I #22 Oct 21 2024 15:17:20
%S 1,1,-49,-149,7201,37001,-1763249,-12863549,604273601,5749693201,
%T -266173427249,-3141020027749,143254364959201,2027866381608601,
%U -91087470841872049,-1510593937967892749,66805009193436144001,1275280159567750343201,-55508977654852972057649
%N Numerator of Hermite(n, 1/10).
%H G. C. Greubel, <a href="/A159247/b159247.txt">Table of n, a(n) for n = 0..450</a> (terms 0..100 from T. D. Noe)
%F From _G. C. Greubel_, Jun 10 2018: (Start)
%F a(n) = 5^n * Hermite(n,1/10).
%F E.g.f.: exp(x-25*x^2).
%F a(n) = numerator(Sum_{k=0..floor(n/2)} (-1)^k*n!*(1/5)^(n-2*k)/(k!*(n-2*k)!)). (End)
%F a(n) = 50*(1-n)*a(n-2)+a(n-1) for n>1. - _Christian Krause_, Oct 21 2024
%t Numerator[Table[HermiteH[n,1/10],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 02 2011*)
%o (PARI) a(n)=numerator(polhermite(n,1/10)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(1/5)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 10 2018
%Y Cf. A158811, A158954, A158960.
%K sign,frac
%O 0,3
%A _N. J. A. Sloane_, Nov 12 2009