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 A059343 Triangle of nonzero coefficients of Hermite polynomials H_n(x) in increasing powers of x. 12
 1, 2, -2, 4, -12, 8, 12, -48, 16, 120, -160, 32, -120, 720, -480, 64, -1680, 3360, -1344, 128, 1680, -13440, 13440, -3584, 256, 30240, -80640, 48384, -9216, 512, -30240, 302400, -403200, 161280, -23040, 1024, -665280, 2217600, -1774080, 506880, -56320, 2048, 665280, -7983360, 13305600 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES 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. L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 50. LINKS T. D. Noe, Rows n=0..100 of triangle, flattened M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy]. M. Janjic, Some classes of numbers and derivatives, JIS 12 (2009) 09.8.3 Eric Weisstein's World of Mathematics, Hermite Polynomial P. Diaconis and A. Gamburd, Random matrices, magic squares and matching polynomials EXAMPLE 1; 2*x; -2+4*x^2; -12*x+8*x^3; ... MAPLE with(orthopoly): h:=proc(n) if n mod 2=0 then expand(x^2*H(n, x)) else expand(x*H(n, x)) fi end: seq(seq(coeff(h(n), x^(2*k)), k=1..1+floor(n/2)), n=0..14); # this gives the signed sequence MATHEMATICA Flatten[ Table[ Coefficient[ HermiteH[n, x], x, k], {n, 0, 12}, {k, Mod[n, 2], n, 2}]] (* Jean-François Alcover, Jan 23 2012 *) PROG (Python) from sympy import hermite, Poly def a(n): return Poly(hermite(n, x), x).coeffs()[::-1] for n in xrange(21): print a(n) # Indranil Ghosh, May 26 2017 CROSSREFS Cf. A059344. If initial zeros are included, same as A060821. Sequence in context: A202795 A256890 A110476 * A285944 A112473 A134435 Adjacent sequences:  A059340 A059341 A059342 * A059344 A059345 A059346 KEYWORD sign,easy,nice,tabf AUTHOR N. J. A. Sloane, Jan 27 2001 EXTENSIONS Edited by Emeric Deutsch, Jun 05 2004 STATUS approved

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Last modified October 19 02:23 EDT 2018. Contains 316327 sequences. (Running on oeis4.)