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%I #11 Sep 08 2022 08:45:11
%S 1,0,-2,-6,-2,90,598,1554,-10082,-164310,-1101242,-1496286,64767118,
%T 965876730,7104497398,57428274,-856472198402,-14195316779190,
%U -122409183339482,25272908324034,21770258523698158
%N Stirling transform of Hermite numbers: Sum_{k=0..n} Stirling2(n,k) * HermiteH(k,0).
%H G. C. Greubel, <a href="/A086660/b086660.txt">Table of n, a(n) for n = 0..500</a>
%F E.g.f.: exp(-(exp(x)-1)^2).
%t Table[Sum[StirlingS2[n,k]HermiteH[k,0],{k,0,n}],{n,0,20}] (* _Harvey P. Dale_, Mar 24 2013 *)
%t With[{nmax = 50}, CoefficientList[Series[Exp[-(Exp[x] - 1)^2], {x, 0, nmax}], x]*Range[0, nmax]!] (* _G. C. Greubel_, Jul 12 2018 *)
%o (PARI) x='x+O('x^50); Vec(serlaplace(exp(-(exp(x)-1)^2))) \\ _G. C. Greubel_, Jul 12 2018
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(-(Exp(x)-1)^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 12 2018
%Y Cf. A067994, A052859.
%K sign
%O 0,3
%A _Vladeta Jovovic_, Sep 12 2003