Search: id:A059344
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%I A059344
%S A059344 1,1,1,2,1,6,1,12,12,1,20,60,1,30,180,120,1,42,420,840,1,56,840,3360,
%T A059344 1680,1,72,1512,10080,15120,1,90,2520,25200,75600,30240,1,110,3960,
%U A059344 55440,277200,332640,1,132,5940,110880,831600,1995840,665280,1,156
%N A059344 Triangle read by rows: row n consists of the nonzero coefficients of 
               the expansion of 2^n x^n in terms of Hermite polynomials with decreasing 
               subscripts.
%D A059344 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.
%D A059344 L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 50.
%H A059344 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].
%F A059344 E.g.f.: exp(x^2+y*x). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 21 
               2003
%F A059344 a(n, k) = n!/(k! (n-2k)!). - Dean Hickerson (dean.hickerson(AT)yahoo.com), 
               Feb 24 2003
%e A059344 1; 1; 1,2; 1,6; 1,12,12; 1,20,60; ...
%e A059344 x^2 = 1/2^2*(Hermite(2,x)+2*Hermite(0,x)); x^3 = 1/2^3*(Hermite(3,x)+6*Hermite(1,
               x)); x^4 = 1/2^4*(Hermite(4,x)+12*Hermite(2,x)+12*Hermite(0,x)); 
               x^5 = 1/2^5*(Hermite(5,x)+20*Hermite(3,x)+60*Hermite(1,x)); x^6 = 
               1/2^6*(Hermite(6,x)+30*Hermite(4,x)+180*Hermite(2,x)+120*Hermite(0,
               x)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 21 2003
%e A059344 1 = H(0); 2x = H(1); 4x^2 = H(2)+2H(0); 8x^3 = H(3)+6H(1); etc. where 
               H(k)=Hermite(k,x).
%t A059344 a[n_, k_] := n!/k!/(n-2k)!; Flatten[Table[a[n, k], {n, 0, 13}, {k, 0, 
               Floor[n/2]}]]
%Y A059344 Cf. A059343, A060821.
%Y A059344 Sequence in context: A139625 A053785 A060173 this_sequence A109193 A083720 
               A055878
%Y A059344 Adjacent sequences: A059341 A059342 A059343 this_sequence A059345 A059346 
               A059347
%K A059344 nonn,easy,nice,tabf
%O A059344 0,4
%A A059344 N. J. A. Sloane (njas(AT)research.att.com), Jan 27 2001
%E A059344 More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 21 2003
%E A059344 Edited by Emeric Deutsch (deutsch(AT)duke.poly.edu), Jun 05 2004

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