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A067613
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Triangular table of coefficients of the Hermite polynomials, divided by 2^floor(n/2).
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0
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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
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OFFSET
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0,3
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COMMENTS
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Series development of exp(-(c+x)^2) at x=0 gives a Hermite polynomial in c as coefficient for x^k.
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LINKS
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Table of n, a(n) for n=0..77.
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FORMULA
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HermiteH[n, c](-1)^n / 2^Floor[n/2]
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MATHEMATICA
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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 ]
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CROSSREFS
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Cf. A060821.
Sequence in context: A097567 A022881 A093201 * A178235 A058531 A093073
Adjacent sequences: A067610 A067611 A067612 * A067614 A067615 A067616
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KEYWORD
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easy,sign,tabl
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AUTHOR
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Wouter Meeussen, Feb 01 2002
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STATUS
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approved
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