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%I #11 Sep 08 2022 08:45:43
%S 1,3,-119,-1125,42321,702963,-24976551,-614805237,20534573985,
%T 691164284643,-21582336376791,-949437293473413,27539617738101489,
%U 1540954535989466835,-41203060308232477191,-2884999709417821999893,70454876663552890207041
%N Numerator of Hermite(n, 3/16).
%H G. C. Greubel, <a href="/A159522/b159522.txt">Table of n, a(n) for n = 0..450</a>
%F From _G. C. Greubel_, Jun 09 2018: (Start)
%F a(n) = 16^n * Hermite(n,3/16).
%F E.g.f.: exp(6*x-252*x^2).
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*(3/8)^(n-2k)/(k!*(n-2k)!). (End)
%t Numerator[Table[HermiteH[n,3/16],{n,0,50}]] (* _Vladimir Joseph Stephan Orlovsky_, Apr 29 2011 *)
%o (PARI) a(n)=numerator(polhermite(n,3/16)) \\ _Charles R Greathouse IV_, Jan 29 2016
%o (Magma) [Numerator((&+[(-1)^k*Factorial(n)*(3/8)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]])): n in [0..30]]; // _G. C. Greubel_, Jun 09 2018
%Y Cf. A159521.
%K sign,frac
%O 0,2
%A _N. J. A. Sloane_, Nov 12 2009