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%I #18 Sep 08 2022 08:45:08
%S 1,6,38,252,1740,12456,92136,702288,5503632,44258400,364615776,
%T 3072862656,26458723008,232501041792,2082933048960,19007627463936,
%U 176533756252416,1667446616360448,16006827410744832,156069042653445120
%N Special values of Hermite polynomials.
%H Vincenzo Librandi, <a href="/A079949/b079949.txt">Table of n, a(n) for n = 0..200</a>
%F In Maple notation, a(n) = I^n*HermiteH(n, -3*I)
%F Recurrence: a(n) = 6*a(n-1) + 2*(n-1)*a(n-2). - _Vaclav Kotesovec_, Oct 13 2012
%F a(n) ~ 2^(n/2-1/2)*exp(-n/2+3*sqrt(2*n)-9/2)*n^(n/2)*(1+3*sqrt(2)/sqrt(n)). - _Vaclav Kotesovec_, Oct 13 2012
%F E.g.f.: exp(x^2+6*x). - _Vaclav Kotesovec_, Oct 21 2012
%p seq(expand(I^n*HermiteH(n,-I*3)),n=0..14);
%t Table[I^n*HermiteH[n, -3I], {n, 0, 20}]
%t CoefficientList[Series[E^(x^2+6*x),{x,0,20}],x]*Range[0,20]! (* _Vaclav Kotesovec_, Oct 21 2012 *)
%o (PARI) x='x+O('x^66); Vec(serlaplace(exp(x^2+6*x))) \\ _Joerg Arndt_, May 07 2013
%o (Magma) m:=50; R<x>:=PowerSeriesRing(Rationals(), m); b:=Coefficients(R!(Exp(6*x + x^2))); [Factorial(n-1)*b[n]: n in [1..m]]; // _G. C. Greubel_, Jul 10 2018
%Y Cf. A000898.
%K nonn
%O 0,2
%A _Karol A. Penson_, Jan 19 2003
%E Edited and extended by _Robert G. Wilson v_, Jan 22 2003
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