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 A067613 Triangular table of coefficients of the Hermite polynomials, divided by 2^floor(n/2). 1
 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, 8, 0, 210, 0, -420, 0, 168, 0, -16, 105, 0, -840, 0, 840, 0, -224, 0, 16, 0, -1890, 0, 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 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Series development of exp(-(c+x)^2) at x=0 gives a Hermite polynomial in c as coefficient for x^k. LINKS Robert Israel, Table of n, a(n) for n = 0..10010(rows 0 to 140, flattened) FORMULA HermiteH[n, c](-1)^n / 2^Floor[n/2] MAPLE S:=series(exp(-2*c*x-x^2), x, 13): 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 MATHEMATICA 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 ] PROG (PARI) row(n) = Vecrev((-1)^n*polhermite(n)/2^floor(n/2)) \\ Michel Marcus, Dec 07 2018 CROSSREFS Cf. A060821. Sequence in context: A022881 A328748 A093201 * A264034 A058531 A093073 Adjacent sequences:  A067610 A067611 A067612 * A067614 A067615 A067616 KEYWORD easy,sign,tabl,look AUTHOR Wouter Meeussen, Feb 01 2002 STATUS approved

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Last modified June 17 17:05 EDT 2021. Contains 345085 sequences. (Running on oeis4.)