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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-Fran├žois 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.)