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
AUTHOR
Wouter Meeussen, Feb 01 2002
STATUS
approved