# looking for simple stuff

Meeussen Wouter (bkarnd) wouter.meeussen at vandemoortele.com
Mon Jan 28 19:45:43 CET 2002

```series development of Exp[-(c+x)^2] at x=0 gives a
polynomial in c as coefficient for x^k,

after some kneading, I got :
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];

ColumnForm[a2] =

{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}
{10395, 0, -124740, 0, 207900, 0, -110880, 0, 23760, 0, -2112, 0, 64}

I feel certain that it's in OEIS somewhere or other, disguised (or
de-funked),
No matter what I tried, no hits!
anyone got any nice ideas? I'd like to get at those polynomials.

all the best,

Wouter

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