%I A060821
%S A060821 1,0,2,2,0,4,0,12,0,8,12,0,48,0,16,0,120,0,160,0,32,120,0,720,0,480,0,
               64,0,
%T A060821 1680,0,3360,0,1344,0,128,1680,0,13440,0,13440,0,3584,0,256,0,30240,0,
               80640,0,
%U A060821 48384,0,9216,0,512,30240,0,302400,0,403200,0,161280,0,23040,0,1024
%V A060821 1,0,2,-2,0,4,0,-12,0,8,12,0,-48,0,16,0,120,0,-160,0,32,-120,0,720,0,-480,
               0,64,0,
%W A060821 -1680,0,3360,0,-1344,0,128,1680,0,-13440,0,13440,0,-3584,0,256,0,30240,
               0,-80640,0,
%X A060821 48384,0,-9216,0,512,-30240,0,302400,0,-403200,0,161280,0,-23040,0,1024
%N A060821 Triangle T(n,k) read by rows giving coefficients of Hermite polynomial 
               of order n (n >= 0, 0 <= k <= n).
%C A060821 Exponential Riordan array [exp(-x^2),2x]. [From Paul Barry (pbarry(AT)wit.ie), 
               Jan 22 2009]
%D A060821 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, 
               National Bureau of Standards Applied Math. Series 55, 1964 (and various 
               reprintings), p. 801.
%H A060821 T. D. Noe, <a href="b060821.txt">Rows n=0..100 of triangle, flattened</
               a>
%H A060821 M. Abramowitz and I. A. Stegun, eds., <a href="http://www.nrbook.com/
               abramowitz_and_stegun/">Handbook of Mathematical Functions</a>, National 
               Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 
               [alternative scanned copy].
%H A060821 R. D. Poshusta, <a href="http://www.poshusta.chem.wsu.edu/DEQU/hermite.htm">
               Hermite Polynomials</a>
%H A060821 <a href="Sindx_He.html#Hermite">Index entries for sequences related to 
               Hermite polynomials</a>
%F A060821 T(n, k)= ((-1)^((n-k)/2))*(2^k)*n!/(k!*((n-k)/2)!) if n-k is even and 
               >=0, else 0.
%F A060821 E.g.f.: exp(-y^2+2*y*x).
%F A060821 T(n, k)=n!/(k!*2^((n-k)/2)((n-k)/2)!)2^((n+k)/2)cos(pi*(n-k)/2)(1+(-1)^(n+k))/
               2; T(n, k)=A001498((n+k)/2, (n-k)/2)*cos(pi*(n-k)/2)2^((n+k)/2)(1+(-1)^(n+k))/
               2; - Paul Barry (pbarry(AT)wit.ie), Aug 28 2005
%e A060821 [1], [0, 2], [ -2, 0, 4], [0, -12, 0, 8], [12, 0, -48, 0, 16], [0, 120, 
               0, -160, 0, 32], ... . Thus H_0(x)=1, H_1(x)=2*x, H_2(x)=-2+4*x^2, 
               H_3(x)=-12*x+8*x^3, H_4(x)=12-48*x^2+16*x^4,...
%p A060821 with(orthopoly):for n from 0 to 10 do H(n,x):od;
%p A060821 T := proc(n,m) if n-m >= 0 and n-m mod 2 = 0 then ((-1)^((n-m)/2))*(2^m)*n!/
               (m!*((n-m)/2)!) else 0 fi; end;
%Y A060821 Cf. A001814, A001816, A000321.
%Y A060821 Without initial zeros, same as A059343.
%Y A060821 Sequence in context: A138090 A138093 A138094 this_sequence A005881 A144458 
               A098268
%Y A060821 Adjacent sequences: A060818 A060819 A060820 this_sequence A060822 A060823 
               A060824
%K A060821 sign,tabl,nice
%O A060821 0,3
%A A060821 Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 30 2001