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A067613 Triangular table of coefficients of the Hermite polynomials, divided by 2^floor(n/2).

%I A067613 #16 Dec 07 2018 12:28:01
%S A067613 1,0,-2,-1,0,2,0,6,0,-4,3,0,-12,0,4,0,-30,0,40,0,-8,-15,0,90,0,-60,0,
%T A067613 8,0,210,0,-420,0,168,0,-16,105,0,-840,0,840,0,-224,0,16,0,-1890,0,
%U A067613 5040,0,-3024,0,576,0,-32,-945,0,9450,0,-12600,0,5040,0,-720,0,32,0,20790,0,-69300,0,55440,0,-15840,0,1760,0,-64
%N A067613 Triangular table of coefficients of the Hermite polynomials, divided by 2^floor(n/2).
%C A067613 Series development of exp(-(c+x)^2) at x=0 gives a Hermite polynomial in c as coefficient for x^k.
%H A067613 Robert Israel, <a href="/A067613/b067613.txt">Table of n, a(n) for n = 0..10010</a>(rows 0 to 140, flattened)
%F A067613 HermiteH[n, c](-1)^n / 2^Floor[n/2]
%p A067613 S:=series(exp(-2*c*x-x^2),x,13):
%p A067613 seq(seq(coeff(coeff(S,x,n)*n!/2^floor(n/2),c,j),j=0..n),n=0..12); # _Robert Israel_, Dec 07 2018
%t A067613 Table[ CoefficientList[ HermiteH[ n, c ], c ](-1)^n/2^Floor[ n/2 ], {n, 0, 12} ] (* or, equivalently *) a1=CoefficientList[ Series[ Exp[ c^2 ]Exp[ -(c+x)^2 ], {x, 0, 12} ], x ]; a2=(CoefficientList[ #, c ]&/@ a1 ) Range[ 0, 12 ]! 2^-Floor[ Range[ 0, 12 ]/2 ]
%o A067613 (PARI) row(n) = Vecrev((-1)^n*polhermite(n)/2^floor(n/2)) \\ _Michel Marcus_, Dec 07 2018
%Y A067613 Cf. A060821.
%K A067613 easy,sign,tabl,look
%O A067613 0,3
%A A067613 _Wouter Meeussen_, Feb 01 2002