Egf. for n!! A006882

[Wouter Meeussen]

by accident, and with help from Christian Bower:

Egf. for (n-1)!! is (1 -  Sqrt[Pi/2] Erf[-x/Sqrt[2]]) Exp[x^2 /2] (sent 
erroneously as Egf for n!! to eisA006882

so the correct Egf. for n!! (A006882)is the derivative of the above:
1+E^(x^2/2) x (1+Sqrt[Pi/2] Erf[x/Sqrt[2]])

check:
In[1]:=CoefficientList[Series[1+E^(x^2/2) x (1+Sqrt[Pi/2] Erf[x/Sqrt[2]]), 
{x, 0, 24}], x]*Range[0, 24]!

Out[1]=
{1, 1, 2, 3, 8, 15, 48, 105, 384, 945, 3840, 10395, 46080, 135135, 645120, 
2027025, 10321920, 34459425, 185794560, 654729075, 3715891200, 13749310575, 
81749606400, 316234143225, 1961990553600}

cheers,

Wouter Meeussen
tel +32 (0)51 33 21 24
fax +32 (0)51 33 21 75
wouter.meeussen at vandemoortele.com