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%I #20 Sep 08 2022 08:45:38
%S 1,4,14,40,76,-16,-824,-3104,-880,46144,200416,-121216,-4894016,
%T -16666880,60576896,708980224,1018614016,-18612911104,-109084520960,
%U 233726715904,5080118660096,10971406004224,-169479359707136,-1160659303014400,3153413334470656
%N a(n) = Hermite(n,2).
%H G. C. Greubel, <a href="/A144141/b144141.txt">Table of n, a(n) for n = 0..729</a>
%F From _G. C. Greubel_, Jul 10 2018: (Start)
%F E.g.f.: exp(4*x - x^2).
%F a(n) = Sum_{k=0..floor(n/2)} (-1)^k*n!*4^(n-2*k)/(k!*(n-2*k)!). (End)
%t lst={};Do[AppendTo[lst,HermiteH[n,2]],{n,0,7^2}];lst
%t HermiteH[Range[0,30],2] (* _Harvey P. Dale_, May 20 2012 *)
%o (PARI) for(n=0, 50, print1(polhermite(n, 2), ", " )) \\ _G. C. Greubel_, Jul 10 2018
%o (Magma) [(&+[(-1)^k*Factorial(n)*(4)^(n-2*k)/( Factorial(k) *Factorial(n-2*k)): k in [0..Floor(n/2)]]): n in [0..30]]; // _G. C. Greubel_, Jul 10 2018
%Y Cf. A000898, A000321, A062267.
%K sign
%O 0,2
%A _Vladimir Joseph Stephan Orlovsky_, Sep 11 2008
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