|
Search: id:A067613
|
|
|
| A067613 |
|
Triangular table of coefficients of the Hermite polynomials, divided by 2^Floor[n/2]. |
|
+0
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; graph; listen)
|
|
|
OFFSET
|
0,3
|
|
|
COMMENT
|
Series development of exp(-(c+x)^2) at x=0 gives a Hermite polynomial in c as coefficient for x^k.
|
|
FORMULA
|
HermiteH[n, c](-1)^n /2^Floor[n/2]
|
|
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 ]
|
|
CROSSREFS
|
Cf. A060821.
Sequence in context: A097567 A022881 A093201 this_sequence A058531 A093073 A156319
Adjacent sequences: A067610 A067611 A067612 this_sequence A067614 A067615 A067616
|
|
KEYWORD
|
easy,sign
|
|
AUTHOR
|
Wouter Meeussen (wouter.meeussen(AT)pandora.be), Feb 01 2002
|
|
|
Search completed in 0.002 seconds
|
