Egf. for n!! A006882
Wouter Meeussen
w.meeussen.vdmcc at vandemoortele.be
Mon Mar 12 12:40:32 CET 2001
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
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